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Theorem an42s 824
Description: Inference rearranging 4 conjuncts in antecedent. (Contributed by NM, 10-Aug-1995.)
Hypothesis
Ref Expression
an41r3s.1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  ->  ta )
Assertion
Ref Expression
an42s  |-  ( ( ( ph  /\  ch )  /\  ( th  /\  ps ) )  ->  ta )

Proof of Theorem an42s
StepHypRef Expression
1 an41r3s.1 . . 3  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  ->  ta )
21an4s 823 . 2  |-  ( ( ( ph  /\  ch )  /\  ( ps  /\  th ) )  ->  ta )
32ancom2s 800 1  |-  ( ( ( ph  /\  ch )  /\  ( th  /\  ps ) )  ->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  nnmsucr  7264  ecopoveq  7402  sbthlem9  7625  mulclsr  9450  mulasssr  9456  distrsr  9457  ltsosr  9460  axmulf  9512  axmulass  9523  axdistr  9524  subadd4  9852  mulsub  9988  mgmidmo  15724  tgcl  19230  bwth  19669  pntibndlem2  23497  hosubadd4  26395  fdc  29828  isdrngo2  29951  unichnidl  30018  acongtr  30507
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