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Given the following axioms:

1) ##P\implies(Q\implies P)##

2) ##((P\implies(Q\implies R))\implies((P\implies Q)\implies(P\implies R))## Where ##P,Q,R## are any formulas

3)##(\neg P\implies\neg Q)\implies (Q\implies P)## then prove:

##\{A\implies B,B\implies C\}|- A\implies C##

Without using the deduction theorem and as a rule of inference M.ponens

1) ##P\implies(Q\implies P)##

2) ##((P\implies(Q\implies R))\implies((P\implies Q)\implies(P\implies R))## Where ##P,Q,R## are any formulas

3)##(\neg P\implies\neg Q)\implies (Q\implies P)## then prove:

##\{A\implies B,B\implies C\}|- A\implies C##

Without using the deduction theorem and as a rule of inference M.ponens

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