1. assumption                      [B⇒(A∨C)]

 2. assumption                      [A∨(¬B∧D)]

 3. assumption                      [D⇒(A∨C)]

 4. assumption                      (C⇒B)

 5. hypothesis  {5}                 ¬A

 6. 2, 5 disjunctive syllogism {5}  (¬B∧D)

 7. 6 conjunction out right {5}     D

 8. 7, 3 detachment {5}             (A∨C)

 9. 5, 8 disjunctive syllogism {5}  C

 10. 9, 4 detachment {5}            B

 11. 6 conjunction out left {5}     ¬B

 12. negation elimination 5, 10, 11 A