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Theorem wl-luk-ax1 34597
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-luk-ax1 (𝜑 → (𝜓𝜑))

Proof of Theorem wl-luk-ax1
StepHypRef Expression
1 ax-luk3 34584 . 2 (𝜑 → (¬ 𝜑 → ¬ 𝜓))
2 wl-luk-ax3 34596 . 2 ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑))
31, 2wl-luk-syl 34587 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 34582  ax-luk2 34583  ax-luk3 34584
This theorem is referenced by:  wl-luk-pm2.27  34598  wl-luk-a1d  34604  wl-luk-pm2.04  34608
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