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Theorem wl-ax1 32923
Description: ax-1 6 proved from Lukasiewicz's axioms. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
wl-ax1 (𝜑 → (𝜓𝜑))

Proof of Theorem wl-ax1
StepHypRef Expression
1 ax-luk3 32910 . 2 (𝜑 → (¬ 𝜑 → ¬ 𝜓))
2 wl-ax3 32922 . 2 ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑))
31, 2wl-syl 32913 1 (𝜑 → (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-pm2.27  32924  wl-a1d  32930  wl-pm2.04  32934
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