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Theorem wl-ax2 33763
Description: ax-2 7 proved from Lukasiewicz's axioms. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
wl-ax2 ((𝜑 → (𝜓𝜒)) → ((𝜑𝜓) → (𝜑𝜒)))

Proof of Theorem wl-ax2
StepHypRef Expression
1 wl-pm2.21 33758 . . 3 𝜑 → (𝜑𝜒))
21wl-a1d 33762 . 2 𝜑 → ((𝜑𝜓) → (𝜑𝜒)))
3 wl-imim2 33761 . 2 ((𝜓𝜒) → ((𝜑𝜓) → (𝜑𝜒)))
42, 3wl-ja 33760 1 ((𝜑 → (𝜓𝜒)) → ((𝜑𝜓) → (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 33740  ax-luk2 33741  ax-luk3 33742
This theorem is referenced by:  wl-pm2.04  33766
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