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Theorem anbi12ci 449
Description: Variant of anbi12i 448 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
anbi12.1  |-  ( ph  <->  ps )
anbi12.2  |-  ( ch  <->  th )
Assertion
Ref Expression
anbi12ci  |-  ( (
ph  /\  ch )  <->  ( th  /\  ps )
)

Proof of Theorem anbi12ci
StepHypRef Expression
1 anbi12.1 . . 3  |-  ( ph  <->  ps )
2 anbi12.2 . . 3  |-  ( ch  <->  th )
31, 2anbi12i 448 . 2  |-  ( (
ph  /\  ch )  <->  ( ps  /\  th )
)
4 ancom 262 . 2  |-  ( ( ps  /\  th )  <->  ( th  /\  ps )
)
53, 4bitri 182 1  |-  ( (
ph  /\  ch )  <->  ( th  /\  ps )
)
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  opelopabsbALT  4022  cnvpom  4890  f1cnvcnv  5131
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