Metamath Proof Explorer


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 ) → ( 𝜓𝜑 ) )

Proof

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