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Theorem syl11 31
Description: A syllogism inference. Commuted form of an instance of syl 14. (Contributed by BJ, 25-Oct-2021.)
Hypotheses
Ref Expression
syl11.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl11.2  |-  ( th 
->  ph )
Assertion
Ref Expression
syl11  |-  ( ps 
->  ( th  ->  ch ) )

Proof of Theorem syl11
StepHypRef Expression
1 syl11.2 . . 3  |-  ( th 
->  ph )
2 syl11.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2syl 14 . 2  |-  ( th 
->  ( ps  ->  ch ) )
43com12 30 1  |-  ( ps 
->  ( 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 7
This theorem is referenced by:  alzdvds  10388
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