Theorem pm2.51 165

Description: Theorem *2.51 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.51	⊢ (¬ (𝜑 → 𝜓) → (𝜑 → ¬ 𝜓))

Proof of Theorem pm2.51

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 ⊢ (𝜓 → (𝜑 → 𝜓))
2	1	con3i 150	. 2 ⊢ (¬ (𝜑 → 𝜓) → ¬ 𝜓)
3	2	a1d 25	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-3 8

This theorem is referenced by:  pm5.12  929