Theorem ax3h 47658

Description: Recover ax-3 8 from hirstL-ax3 47657. (Contributed by Jarvin Udandy, 3-Jul-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
ax3h	⊢ ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑))

Proof of Theorem ax3h

Step	Hyp	Ref	Expression
1		hirstL-ax3 47657	. 2 ⊢ ((¬ 𝜑 → ¬ 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜑))
2		jarr 107	. 2 ⊢ (((¬ 𝜑 → 𝜓) → 𝜑) → (𝜓 → 𝜑))
3	1, 2	syl 18	1 ⊢ ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑))

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 proof depends on definitions:  df-bi 210  df-or 861

This theorem is used by: (None)