Theorem pm3.2im 627

Description: In classical logic, this is just a restatement of pm3.2 138. In intuitionistic logic, it still holds, but is weaker than pm3.2. (Contributed by Mario Carneiro, 12-May-2015.)

Assertion

Ref	Expression
pm3.2im	⊢ (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))

Proof of Theorem pm3.2im

Step	Hyp	Ref	Expression
1		pm2.27 40	. 2 ⊢ (𝜑 → ((𝜑 → ¬ 𝜓) → ¬ 𝜓))
2	1	con2d 614	1 ⊢ (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 604  ax-in2 605

This theorem is referenced by:  expi  628  jc  640  expt  647  imnan  680  dfandc  874