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Theorem wl-luk-pm2.18d 34578
Description: Deduction based on reductio ad absurdum. Copy of pm2.18d 127 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
wl-luk-pm2.18d.1 (𝜑 → (¬ 𝜓𝜓))
Assertion
Ref Expression
wl-luk-pm2.18d (𝜑𝜓)

Proof of Theorem wl-luk-pm2.18d
StepHypRef Expression
1 wl-luk-pm2.18d.1 . 2 (𝜑 → (¬ 𝜓𝜓))
2 ax-luk2 34572 . 2 ((¬ 𝜓𝜓) → 𝜓)
31, 2wl-luk-syl 34576 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 34571  ax-luk2 34572
This theorem is referenced by:  wl-luk-con4i  34579  wl-luk-mpi  34582  wl-luk-con1i  34590  wl-luk-ja  34591
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