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Theorem wl-ax3 32922
Description: ax-3 8 proved from Lukasiewicz's axioms. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
wl-ax3 ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑))

Proof of Theorem wl-ax3
StepHypRef Expression
1 ax-luk3 32910 . . 3 (𝜓 → (¬ 𝜓𝜑))
2 ax-luk1 32908 . . 3 ((¬ 𝜑 → ¬ 𝜓) → ((¬ 𝜓𝜑) → (¬ 𝜑𝜑)))
31, 2wl-syl5 32914 . 2 ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → (¬ 𝜑𝜑)))
4 ax-luk2 32909 . 2 ((¬ 𝜑𝜑) → 𝜑)
53, 4wl-syl6 32921 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-luk1 32908  ax-luk2 32909  ax-luk3 32910
This theorem is referenced by:  wl-ax1  32923
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