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Theorem wl-pm2.27 33624
Description: This theorem, called "Assertion", can be thought of as closed form of modus ponens ax-mp 5. Theorem *2.27 of [WhiteheadRussell] p. 104. Copy of pm2.27 42 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
wl-pm2.27 (𝜑 → ((𝜑𝜓) → 𝜓))

Proof of Theorem wl-pm2.27
StepHypRef Expression
1 wl-ax1 33623 . . 3 (𝜑 → (¬ 𝜓𝜑))
2 ax-luk1 33608 . . 3 ((¬ 𝜓𝜑) → ((𝜑𝜓) → (¬ 𝜓𝜓)))
31, 2wl-syl 33613 . 2 (𝜑 → ((𝜑𝜓) → (¬ 𝜓𝜓)))
4 ax-luk2 33609 . 2 ((¬ 𝜓𝜓) → 𝜓)
53, 4wl-syl6 33621 1 (𝜑 → ((𝜑𝜓) → 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 33608  ax-luk2 33609  ax-luk3 33610
This theorem is referenced by:  wl-com12  33625
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