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Theorem anbi2ci 696
Description: Variant of anbi2i 694 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Hypothesis
Ref Expression
anbi.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
anbi2ci  |-  ( (
ph  /\  ch )  <->  ( ch  /\  ps )
)

Proof of Theorem anbi2ci
StepHypRef Expression
1 anbi.1 . . 3  |-  ( ph  <->  ps )
21anbi1i 695 . 2  |-  ( (
ph  /\  ch )  <->  ( ps  /\  ch )
)
3 ancom 450 . 2  |-  ( ( ps  /\  ch )  <->  ( ch  /\  ps )
)
42, 3bitri 249 1  |-  ( (
ph  /\  ch )  <->  ( ch  /\  ps )
)
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  clabel  2589  disjxun  4435  asymref  5373  ordpwsuc  6635  supmo  7914  kmlem3  8535  cfval2  8643  eqger  16125  gaorber  16220  opprunit  17184  xmeter  20809  usgra2pth0  32193  alimp-no-surprise  32926  bj-ifn  33897  bj-clabel  34111
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