Theorem conax1k 172

Description: Weakening of conax1 171. General instance of pm2.51 173 and of pm2.52 174. (Contributed by BJ, 28-Oct-2023.)

Assertion

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

Proof of Theorem conax1k

Step	Hyp	Ref	Expression
1		conax1 171	. 2 ⊢ (¬ (𝜑 → 𝜓) → ¬ 𝜓)
2	1	a1d 26	1 ⊢ (¬ (𝜑 → 𝜓) → (𝜒 → ¬ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  pm2.51  173  pm2.52  174