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Theorem syl5imp 39238
Description: Closed form of syl5 34. Derived automatically from syl5impVD 39616. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
syl5imp ((𝜑 → (𝜓𝜒)) → ((𝜃𝜓) → (𝜑 → (𝜃𝜒))))

Proof of Theorem syl5imp
StepHypRef Expression
1 pm2.04 90 . . 3 ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))
21imim2d 57 . 2 ((𝜑 → (𝜓𝜒)) → ((𝜃𝜓) → (𝜃 → (𝜑𝜒))))
32com34 91 1 ((𝜑 → (𝜓𝜒)) → ((𝜃𝜓) → (𝜑 → (𝜃𝜒))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by: (None)
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