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Theorem wl-syl5 32914
Description: A syllogism rule of inference. The first premise is used to replace the second antecedent of the second premise. Copy of syl5 34 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
wl-syl5.1 (𝜑𝜓)
wl-syl5.2 (𝜒 → (𝜓𝜃))
Assertion
Ref Expression
wl-syl5 (𝜒 → (𝜑𝜃))

Proof of Theorem wl-syl5
StepHypRef Expression
1 wl-syl5.2 . 2 (𝜒 → (𝜓𝜃))
2 wl-syl5.1 . . 3 (𝜑𝜓)
32wl-imim1i 32912 . 2 ((𝜓𝜃) → (𝜑𝜃))
41, 3wl-syl 32913 1 (𝜒 → (𝜑𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 32908
This theorem is referenced by:  wl-con4i  32916  wl-mpi  32919  wl-ax3  32922  wl-com12  32925  wl-con1i  32927  wl-ja  32928  wl-pm2.04  32934
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