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Theorem wl-com12 32890
Description: Inference that swaps (commutes) antecedents in an implication. Copy of com12 32 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
wl-com12.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
wl-com12 (𝜓 → (𝜑𝜒))

Proof of Theorem wl-com12
StepHypRef Expression
1 wl-com12.1 . 2 (𝜑 → (𝜓𝜒))
2 wl-pm2.27 32889 . 2 (𝜓 → ((𝜓𝜒) → 𝜒))
31, 2wl-syl5 32879 1 (𝜓 → (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 32873  ax-luk2 32874  ax-luk3 32875
This theorem is referenced by:  wl-pm2.21  32891  wl-imim2  32894
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