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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  2557  disjxun  4210  ordpwsuc  4795  asymref  5250  supmo  7457  kmlem3  8032  cfval2  8140  eqger  14990  gaorber  15085  opprunit  15766  xmeter  18463  usgra2pth0  28312
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
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