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Theorem wl-mpi 33589
Description: A nested modus ponens inference. Copy of mpi 20 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
wl-mpi.1 𝜓
wl-mpi.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
wl-mpi (𝜑𝜒)

Proof of Theorem wl-mpi
StepHypRef Expression
1 wl-mpi.1 . . . 4 𝜓
21wl-a1i 33588 . . 3 𝜒𝜓)
3 wl-mpi.2 . . 3 (𝜑 → (𝜓𝜒))
42, 3wl-syl5 33584 . 2 (𝜑 → (¬ 𝜒𝜒))
54wl-pm2.18d 33585 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 33578  ax-luk2 33579  ax-luk3 33580
This theorem is referenced by:  wl-imim2i  33590
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