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Theorem an4 520
Description: Rearrangement of 4 conjuncts. (Contributed by NM, 10-Jul-1994.)
Assertion
Ref Expression
an4  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  th )
) )

Proof of Theorem an4
StepHypRef Expression
1 an12 495 . . 3  |-  ( ( ps  /\  ( ch 
/\  th ) )  <->  ( ch  /\  ( ps  /\  th ) ) )
21anbi2i 430 . 2  |-  ( (
ph  /\  ( ps  /\  ( ch  /\  th ) ) )  <->  ( ph  /\  ( ch  /\  ( ps  /\  th ) ) ) )
3 anass 381 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )
4 anass 381 . 2  |-  ( ( ( ph  /\  ch )  /\  ( ps  /\  th ) )  <->  ( ph  /\  ( ch  /\  ( ps  /\  th ) ) ) )
52, 3, 43bitr4i 201 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  th )
) )
Colors of variables: wff set class
Syntax hints:    /\ wa 97    <-> wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  an42  521  an4s  522  anandi  524  anandir  525  rnlem  883  an6  1216  2eu4  1993  reean  2478  reu2  2729  rmo4  2734  rmo3  2849  inxp  4470  xp11m  4759  fununi  4967  fun  5063  resoprab2  5598  xporderlem  5852  poxp  5853  th3qlem1  6208  enq0enq  6529  enq0tr  6532  genpdisj  6621  cju  7913  elfzo2  9007
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