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Theorem an42 798
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 797 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  th )
) )
2 ancom 437 . . 3  |-  ( ( ps  /\  th )  <->  ( th  /\  ps )
)
32anbi2i 675 . 2  |-  ( ( ( ph  /\  ch )  /\  ( ps  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( th  /\  ps )
) )
41, 3bitri 240 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( th  /\  ps )
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358
This theorem is referenced by:  rnlem  931  brecop2  6752  supmo  7203  aceq1  7744  an43  26712  anandii  29107
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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