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Theorem 3com12d 26322
Description: Commutation in consequent. Swap 1st and 2nd. (Contributed by Jeff Hankins, 17-Nov-2009.)
Hypothesis
Ref Expression
3com12d.1  |-  ( ph  ->  ( ps  /\  ch  /\ 
th ) )
Assertion
Ref Expression
3com12d  |-  ( ph  ->  ( ch  /\  ps  /\ 
th ) )

Proof of Theorem 3com12d
StepHypRef Expression
1 3com12d.1 . 2  |-  ( ph  ->  ( ps  /\  ch  /\ 
th ) )
2 id 19 . . 3  |-  ( ( ch  /\  ps  /\  th )  ->  ( ch  /\ 
ps  /\  th )
)
323com12 1155 . 2  |-  ( ( ps  /\  ch  /\  th )  ->  ( ch  /\ 
ps  /\  th )
)
41, 3syl 15 1  |-  ( ph  ->  ( ch  /\  ps  /\ 
th ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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