Theorem conax1 170

Description: Contrapositive of ax-1 6. (Contributed by BJ, 28-Oct-2023.)

Assertion

Ref	Expression
conax1	⊢ (¬ (𝜑 → 𝜓) → ¬ 𝜓)

Proof of Theorem conax1

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜓 → (𝜑 → 𝜓))
2	1	con3i 154	1 ⊢ (¬ (𝜑 → 𝜓) → ¬ 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:  conax1k  171  pm2.521g  174  antnest  35695