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Theorem syl5imp 28274
Description: Closed form of syl5 28. Derived automatically from syl5impVD 28639. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
syl5imp  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( th  ->  ps )  ->  ( ph  ->  ( th  ->  ch )
) ) )

Proof of Theorem syl5imp
StepHypRef Expression
1 pm2.04 76 . . 3  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ps  ->  ( ph  ->  ch ) ) )
21imim2d 48 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( th  ->  ps )  ->  ( th  ->  (
ph  ->  ch ) ) ) )
32com34 77 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( th  ->  ps )  ->  ( ph  ->  ( th  ->  ch )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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