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Theorem an42 552
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 551 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  th )
) )
2 ancom 262 . . 3  |-  ( ( ps  /\  th )  <->  ( th  /\  ps )
)
32anbi2i 445 . 2  |-  ( ( ( ph  /\  ch )  /\  ( ps  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( th  /\  ps )
) )
41, 3bitri 182 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( th  /\  ps )
) )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103
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
This theorem is referenced by:  rnlem  918  supmoti  6465  distrnqg  6639  distrnq0  6711  prcdnql  6736  prcunqu  6737
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