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Theorem anbi2ci 454
Description: Variant of anbi2i 452 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 453 . 2  |-  ( (
ph  /\  ch )  <->  ( ps  /\  ch )
)
3 ancom 264 . 2  |-  ( ( ps  /\  ch )  <->  ( ch  /\  ps )
)
42, 3bitri 183 1  |-  ( (
ph  /\  ch )  <->  ( ch  /\  ps )
)
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  clabel  2266  ordpwsucss  4482  asymref  4924  supmoti  6880  xmeter  12615
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