Theorem axL3.SH 32

Description: Inference from ax-L3 13.

Hypothesis

Ref	Expression
axL3.SH.1	⊢ (¬ 𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
axL3.SH	⊢ (𝜓 → 𝜑)

Proof of Theorem axL3.SH

Step	Hyp	Ref	Expression
1		axL3.SH.1	. 2 ⊢ (¬ 𝜑 → ¬ 𝜓)
2		ax-L3 13	. 2 ⊢ ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑))
3	1, 2	ax-MP 14	1 ⊢ (𝜓 → 𝜑)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

This theorem was proved from axioms:  ax-L3 13  ax-MP 14

This theorem is referenced by:  dneg-P1.13b  72