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Theorem 3com13 1144
Description: Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)
Hypothesis
Ref Expression
3exp.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
3com13  |-  ( ( ch  /\  ps  /\  ph )  ->  th )

Proof of Theorem 3com13
StepHypRef Expression
1 3anrev 930 . 2  |-  ( ( ch  /\  ps  /\  ph )  <->  ( ph  /\  ps  /\  ch ) )
2 3exp.1 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
31, 2sylbi 119 1  |-  ( ( ch  /\  ps  /\  ph )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  3coml  1146  3adant3l  1166  3adant3r  1167  syld3an1  1216  oaword1  6115  nnacan  6151  subadd  7378  xrltso  8947  iooshf  9051  dvdsmulc  10368  lcmdvdsb  10610
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