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Theorem wl-con4i 32916
Description: Inference rule. Copy of con4i 113 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
wl-con4i.1 𝜑 → ¬ 𝜓)
Assertion
Ref Expression
wl-con4i (𝜓𝜑)

Proof of Theorem wl-con4i
StepHypRef Expression
1 wl-con4i.1 . . 3 𝜑 → ¬ 𝜓)
2 ax-luk3 32910 . . 3 (𝜓 → (¬ 𝜓𝜑))
31, 2wl-syl5 32914 . 2 (𝜓 → (¬ 𝜑𝜑))
43wl-pm2.18d 32915 1 (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-a1i  32918
  Copyright terms: Public domain W3C validator