axioms.hpp:
    struct Axiom {}
    void foo(Axiom);

expr.hpp:
    struct Expr;
    void bar(Expr) {}

axioms.cpp
    #include "axioms.hpp"
    #include "expr.hpp"

    void foo(Axiom a) {
        bar(a.e);
    }

expr.cpp
    #include "axioms.hpp"
    #include "expr.hpp"

    void bar(Expr e) {
        foo(e.axiom);
    }