Theorem pm2.51 581

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 5	. . 3 ⊢ (𝜓 → (𝜑 → 𝜓))
2	1	con3i 562	. 2 ⊢ (¬ (𝜑 → 𝜓) → ¬ 𝜓)
3	2	a1d 22	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-in1 544  ax-in2 545

This theorem is referenced by: (None)