Theorem ax3h

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

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

Proof

Step	Hyp	Ref	Expression
1		hirstL-ax3	⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) → ( ( ¬ 𝜑 → 𝜓 ) → 𝜑 ) )
2		jarr	⊢ ( ( ( ¬ 𝜑 → 𝜓 ) → 𝜑 ) → ( 𝜓 → 𝜑 ) )
3	1 2	syl	⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) → ( 𝜓 → 𝜑 ) )