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Theorem syl2imc 39
Description: A commuted version of syl2im 38. Implication-only version of syl2anr 288. (Contributed by BJ, 20-Oct-2021.)
Hypotheses
Ref Expression
syl2im.1  |-  ( ph  ->  ps )
syl2im.2  |-  ( ch 
->  th )
syl2im.3  |-  ( ps 
->  ( th  ->  ta ) )
Assertion
Ref Expression
syl2imc  |-  ( ch 
->  ( ph  ->  ta ) )

Proof of Theorem syl2imc
StepHypRef Expression
1 syl2im.1 . . 3  |-  ( ph  ->  ps )
2 syl2im.2 . . 3  |-  ( ch 
->  th )
3 syl2im.3 . . 3  |-  ( ps 
->  ( th  ->  ta ) )
41, 2, 3syl2im 38 . 2  |-  ( ph  ->  ( ch  ->  ta ) )
54com12 30 1  |-  ( ch 
->  ( ph  ->  ta ) )
Colors of variables: wff set 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:  cnptopco  12380
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