Theorem conax1 171

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 155	1 ⊢ (¬ (𝜑 → 𝜓) → ¬ 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:  conax1k  172  pm2.521g  175  antnest  36218  antnestlaw3lem  36219  antnestlaw1  36220  antnestlaw2  36221