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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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