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Theorem an42 577
Description: Rearrangement of 4 conjuncts. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
an42  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( th  /\  ps )
) )

Proof of Theorem an42
StepHypRef Expression
1 an4 576 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  th )
) )
2 ancom 264 . . 3  |-  ( ( ps  /\  th )  <->  ( th  /\  ps )
)
32anbi2i 453 . 2  |-  ( ( ( ph  /\  ch )  /\  ( ps  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( th  /\  ps )
) )
41, 3bitri 183 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( th  /\  ps )
) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104
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:  rnlem  961  supmoti  6884  distrnqg  7215  distrnq0  7287  prcdnql  7312  prcunqu  7313
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