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Theorem wl-syl 32913
Description: An inference version of the transitive laws for implication luk-1 1577. Copy of syl 17 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
wl-syl.1 (𝜑𝜓)
wl-syl.2 (𝜓𝜒)
Assertion
Ref Expression
wl-syl (𝜑𝜒)

Proof of Theorem wl-syl
StepHypRef Expression
1 wl-syl.2 . 2 (𝜓𝜒)
2 wl-syl.1 . . 3 (𝜑𝜓)
32wl-imim1i 32912 . 2 ((𝜓𝜒) → (𝜑𝜒))
41, 3ax-mp 5 1 (𝜑𝜒)
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-syl5  32914  wl-pm2.18d  32915  wl-syl6  32921  wl-ax1  32923  wl-pm2.27  32924  wl-a1d  32930  wl-id  32932
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