Q:

Propositional Logic Proof

how to prove this statement using propositional logic. The idea is in my head but i just can't seem to figure it out. Here is the statement : 
(A->B)^(B->(C->D))^(A->(B->C))->(A->D)
This is what i've got so far 

A->B  (hyp)
B->(C->D)       (hyp)
A->(B->C)       (hyp)
A               (hyp,DM)
B->C            (3,4,MP)

A:

I use Polish notation.
The problem, as I understand it is to prove CKKCabCbCcdCaCbcCad.  The notation Ko indicates a use of conjunction elimination.  Co indicates a use of detachment (or modus ponens).  Ci indicates the use of conditional introduction.
1  KKCabCbCcdCaCbc  hypothesis
2  a                hypothesis
3  KCabCbCcd        1 Ko-left
4  CaCbc            1 Ko-right
5  Cab              3 Ko-left
6  CbCcd            3 Ko-right
7  Cbc              4, 2 Co
8  b                5, 2 Co
9  c                7, 8 Co
10 Ccd              6, 8 Co
11 d                10, 9 Co
12 Cad              2-11 Ci

A consequence of the deduction metatheorem here tells us that for the system {CpCqp, CCpCqrCCpqCpr, CKpqp, CKpqq} under detachment and uniform substitution CKKCabCbCcdCaCbcCad is a theorem.

