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Theorem syldc 45
Description: Syllogism deduction. Commuted form of syld 44. (Contributed by BJ, 25-Oct-2021.)
Hypotheses
Ref Expression
syld.1  |-  ( ph  ->  ( ps  ->  ch ) )
syld.2  |-  ( ph  ->  ( ch  ->  th )
)
Assertion
Ref Expression
syldc  |-  ( ps 
->  ( ph  ->  th )
)

Proof of Theorem syldc
StepHypRef Expression
1 syld.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
2 syld.2 . . 3  |-  ( ph  ->  ( ch  ->  th )
)
31, 2syld 44 . 2  |-  ( ph  ->  ( ps  ->  th )
)
43com12 30 1  |-  ( ps 
->  ( ph  ->  th )
)
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: (None)
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