Theorem conax1k 644

Description: Weakening of conax1 643. General instance of pm2.51 645 and of pm2.52 646. (Contributed by BJ, 28-Oct-2023.)

Assertion

Ref	Expression
conax1k	⊢ (¬ (𝜑 → 𝜓) → (𝜒 → ¬ 𝜓))

Proof of Theorem conax1k

Step	Hyp	Ref	Expression
1		conax1 643	. 2 ⊢ (¬ (𝜑 → 𝜓) → ¬ 𝜓)
2	1	a1d 22	1 ⊢ (¬ (𝜑 → 𝜓) → (𝜒 → ¬ 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:  pm2.51  645  pm2.52  646