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Theorem wl-luk-imtrid 35107
 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-luk-imtrid.1 (𝜑𝜓)
wl-luk-imtrid.2 (𝜒 → (𝜓𝜃))
Assertion
Ref Expression
wl-luk-imtrid (𝜒 → (𝜑𝜃))

Proof of Theorem wl-luk-imtrid
StepHypRef Expression
1 wl-luk-imtrid.2 . 2 (𝜒 → (𝜓𝜃))
2 wl-luk-imtrid.1 . . 3 (𝜑𝜓)
32wl-luk-imim1i 35105 . 2 ((𝜓𝜃) → (𝜑𝜃))
41, 3wl-luk-syl 35106 1 (𝜒 → (𝜑𝜃))
 Colors of variables: wff setvar class Syntax hints:   → wi 4 This theorem was proved from axioms:  ax-mp 5  ax-luk1 35101 This theorem is referenced by:  wl-luk-con4i  35109  wl-luk-mpi  35112  wl-luk-ax3  35115  wl-luk-com12  35118  wl-luk-con1i  35120  wl-luk-ja  35121  wl-luk-pm2.04  35127
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