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Theorem ax3h 40380
Description: Recovery of ax-3 8 from hirstL-ax3 40379. (Contributed by Jarvin Udandy, 3-Jul-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax3h ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑))

Proof of Theorem ax3h
StepHypRef Expression
1 hirstL-ax3 40379 . 2 ((¬ 𝜑 → ¬ 𝜓) → ((¬ 𝜑𝜓) → 𝜑))
2 jarr 106 . 2 (((¬ 𝜑𝜓) → 𝜑) → (𝜓𝜑))
31, 2syl 17 1 ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-or 385
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator