Prove the 2nd axiom of mathematical logic using the Deduction Theorem

AI Thread Summary
The discussion focuses on proving the second axiom of mathematical logic, which states that if P implies (Q implies R), then if P implies Q, it follows that P implies R. Participants emphasize the importance of using the Deduction Theorem for this proof. There's a consensus that axioms are foundational and should precede theorems in logical reasoning. Some users express skepticism about attempting the proof in reverse, suggesting that progress should be shared for constructive feedback. The conversation highlights the structured approach necessary for logical proofs in mathematical contexts.
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prove:
The 2nd axiom of mathematical logic

2) $((P\implies(Q\implies R))\implies((P\implies Q)\implies(P\implies R))$

By using only the deduction theorem
 
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Axioms come before theorems so there isn't much point, but if you still want to do this backwards then show us what progress you have made.
 

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