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Theorem an12 561
Description: Swap two conjuncts. Note that the first digit (1) in the label refers to the outer conjunct position, and the next digit (2) to the inner conjunct position. (Contributed by NM, 12-Mar-1995.)
Assertion
Ref Expression
an12  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ps  /\  ( ph  /\  ch ) ) )

Proof of Theorem an12
StepHypRef Expression
1 ancom 266 . . 3  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
21anbi1i 458 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ps  /\  ph )  /\  ch ) )
3 anass 401 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ph  /\  ( ps  /\  ch ) ) )
4 anass 401 . 2  |-  ( ( ( ps  /\  ph )  /\  ch )  <->  ( ps  /\  ( ph  /\  ch ) ) )
52, 3, 43bitr3i 210 1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ps  /\  ( ph  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 104    <-> wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  an32  562  an13  563  an12s  565  an4  586  ceqsrexv  2868  rmoan  2938  2reuswapdc  2942  reuind  2943  2rmorex  2944  sbccomlem  3038  elunirab  3823  rexxfrd  4464  opeliunxp  4682  elres  4944  resoprab  5971  ov6g  6012  opabex3d  6122  opabex3  6123  xpassen  6830  distrnqg  7386  distrnq0  7458  rexuz2  9581  2clim  11309  issubrg  13342  isbasis2g  13548  tgval2  13554
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