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Theorem an12s 555
Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 551 is combined with syl 14 (or a variant). (Contributed by NM, 13-Mar-1996.)
Hypothesis
Ref Expression
an12s.1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
Assertion
Ref Expression
an12s  |-  ( ( ps  /\  ( ph  /\ 
ch ) )  ->  th )

Proof of Theorem an12s
StepHypRef Expression
1 an12 551 . 2  |-  ( ( ps  /\  ( ph  /\ 
ch ) )  <->  ( ph  /\  ( ps  /\  ch ) ) )
2 an12s.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylbi 120 1  |-  ( ( ps  /\  ( ph  /\ 
ch ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anabsan2  574  1stconst  6168  2ndconst  6169  sbthlemi5  6905  iccshftr  9898  iccshftl  9900  iccdil  9902  icccntr  9904  zfz1iso  10712  ndvdsadd  11822  neipsm  12565
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