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Theorem anbi2ci 678
Description: Variant of anbi2i 676 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Hypothesis
Ref Expression
bi.aa  |-  ( ph  <->  ps )
Assertion
Ref Expression
anbi2ci  |-  ( (
ph  /\  ch )  <->  ( ch  /\  ps )
)

Proof of Theorem anbi2ci
StepHypRef Expression
1 bi.aa . . 3  |-  ( ph  <->  ps )
21anbi1i 677 . 2  |-  ( (
ph  /\  ch )  <->  ( ps  /\  ch )
)
3 ancom 438 . 2  |-  ( ( ps  /\  ch )  <->  ( ch  /\  ps )
)
42, 3bitri 241 1  |-  ( (
ph  /\  ch )  <->  ( ch  /\  ps )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359
This theorem is referenced by:  clabel  2508  disjxun  4151  ordpwsuc  4735  asymref  5190  supmo  7390  kmlem3  7965  cfval2  8073  eqger  14917  gaorber  15012  opprunit  15693  xmeter  18353
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 178  df-an 361
  Copyright terms: Public domain W3C validator