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Theorem wl-luk-syl 35238
Description: An inference version of the transitive laws for implication luk-1 1662. 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-luk-syl.1 (𝜑𝜓)
wl-luk-syl.2 (𝜓𝜒)
Assertion
Ref Expression
wl-luk-syl (𝜑𝜒)

Proof of Theorem wl-luk-syl
StepHypRef Expression
1 wl-luk-syl.2 . 2 (𝜓𝜒)
2 wl-luk-syl.1 . . 3 (𝜑𝜓)
32wl-luk-imim1i 35237 . 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 35233
This theorem is referenced by:  wl-luk-imtrid  35239  wl-luk-pm2.18d  35240  wl-luk-imtrdi  35246  wl-luk-ax1  35248  wl-luk-pm2.27  35249  wl-luk-a1d  35255  wl-luk-id  35257
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