Validate form with AJAX, prevent form submitting on conditio

index.php
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<form onsubmit="return false"  class="form-horizontal" name="ads_post" id="post_form"  method="post">
<div class="form-group">
      <label class="control-label col-sm-2" >Name</label>
      <div class="col-sm-10">
       <input type="text" class="form-control" id="name"  placeholder="Enter Name" name="user_name">

      </div>
      <span class="name_error"></span>
    </div>


    <div class="form-group">
      <label class="control-label col-sm-2" >email</label>
      <div class="col-sm-10">
        <input type="email" class="form-control" id="email"  placeholder="Enter email" name="email">
      </div>
      <span class="mail_error"></span>
    </div>

</form>
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validate.js
----------------------------------------------------------------------------------------------------------------------------
$(document).ready(function(){
  function verify_name(name){
    $(".name_error").hide();
    if(name == ""){
    $(".name_error").show();
    $(".name_error").html("plz provide your name");

    }

   else{

    $(".name_error").show();
    $(".name_error").html("validating......");
    $.ajax({
    url:"classes/process.php",
    method:"post",
    data:{check_name:1,name:name},
    success:function(data){

    $(".name_error").show();
    if(data == "invalid_name"){
    $(".name_error").html("Plz provide valid name");


    }
    else if(data == "good"){$(".name_error").html("ok");

    }
    },error: function(req, status, error) {
          // alert('Error: ' + req.status);
            console.log(error);
            console.log();
            }

    })
   }

}

   function verify_email(email){

    $(".mail_error").hide();
    if(email == ""){
    $(".mail_error").show();
    $(".mail_error").html("plz provide your Email");

    }
    else{
    $(".mail_error").show();
    $(".mail_error").html("validating......");

    $.ajax({
    url:"classes/process.php",
    method:"post",
    data:{check_email:1,email:email},
    success:function(data){

    $(".mail_error").show();
    if(data == "already_exists"){
    $(".mail_error").html("Email Already Exists Plz try another");
    }else if(data == "invalid_email"){

    $(".mail_error").html("Email Provided is Invalid");

    }
   else if(data == "ok"){
    $(".mail_error").html("ok");

    }
    },error: function(req, status, error) {
          // alert('Error: ' + req.status);
            console.log(error);
            console.log();
            }

    })
   }


   }

$("#name").focusout(function(){
    var name=$("#name").val();
    verify_name(name);

    })

    $("#email").focusout(function(){
    var email=$("#email").val();
    verify_email(email);

      })



$("#post_form").on("submit",function(){

    var name = $("#name").val();
    var email = $("#email").val();

    if(name == ""){
     $(".name_error").show();
     $(".name_error").html("plz provide your name");

    }

    else if(email == ""){
    $(".mail_error").show();
    $(".mail_error").html("plz provide your email");

    }

    else{

    $.ajax({
          url:"classes/process.php",
          method:"post",
          data:$("#post_form").serialize(),
          success:function(data){
          //if(data=="ok"){
          //window.location.href="index.php";
          alert(data);
          //}
          },error: function(req, status, error) {
          // alert('Error: ' + req.status);
            console.log(error);
            console.log();
            }

         })


    }
      })
})

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process.php
----------------------------------------------------------------------------------------------------------------
<?php

include "dbcon.php";

class DataOperation extends database{

public $num_rec_per_page=1;

public function insert_record($table,$fields){

    $sql="";
    $sql.="insert into ".$table ;
    $sql.=" (".implode(",",array_keys($fields)).") values ";
    $sql.="(' ".implode(" ',' ",array_values($fields))." ' )";
    $query=mysqli_query($this->con,$sql);
    $id = mysqli_insert_id($this->con);

        if ($query){
                  return $id;
              }

    }

public function verify_email($table,$email){
    //[email protected]
     $regexp = "/^[a-z0-9_-]+(\.[a-z0-9_-]+)*@[a-z0-9-]+(\.[a-z0-9-]+)*(\.[a-z]{2,4})$/";
     if(!preg_match($regexp,$email)){
     return "invalid_email";

     }
     //select id from user_info WHERE u_email = '[email protected] ' LIMIT 1";
     //check email already exists or not
     $sql = "select id from ".$table." WHERE email = '$email' LIMIT 1";
     $query = mysqli_query($this->con,$sql) or die (mysqli_error($this->con));
     $count = mysqli_num_rows($query);
     if($count == 0){

     return "ok";

     }else{
     return "already_exists";
     }

    }
    public function verify_name($name){
    //[email protected]
     $regexp = "/^[A-Za-z_]{2,5}$/";
     //if(!preg_match($regexp,$name)){
     //return "invalid_name";
     return (!preg_match($regexp,$name)) ? "invalid_name" : 'good';


    }

}

$obj = new DataOperation;


 if(isset($_POST["check_email"])){
     $email=$_POST["email"];
     echo $data=$obj->verify_email("user",$email);
     exit();
 }

   if(isset($_POST["check_name"])){
     $name=$_POST["name"];
     echo $data=$obj->verify_name($name);
     exit();
 }

if(isset($_POST["user_name"])){
$name= $_POST["user_name"];

$data=$obj->verify_email("user",$_POST["email"]);
         if($data == "already_exists"){
             echo "Email Already Exists Plz try other";
             exit();
            }else{
            echo $email= $_POST["email"];
        }

$user_info = array(
                "name_user" => $name,

                "email" => $email,

                );
                if ($obj->insert_record("user",$myarray)) {
                //header("location:../index.php?msg=Successfully inserted");
                echo "success";
                exit();
                }


}