Theorem pm2.52 582

Description: Theorem *2.52 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
pm2.52	⊢ (¬ (𝜑 → 𝜓) → (¬ 𝜑 → ¬ 𝜓))

Proof of Theorem pm2.52

Step	Hyp	Ref	Expression
1		pm2.21 547	. . 3 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2	1	pm2.24d 552	. 2 ⊢ (¬ 𝜑 → (¬ (𝜑 → 𝜓) → ¬ 𝜓))
3	2	com12 27	1 ⊢ (¬ (𝜑 → 𝜓) → (¬ 𝜑 → ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in2 545

This theorem is referenced by:  pm2.521dc  764