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

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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.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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