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Theorem anbi12ci 442
Description: Variant of anbi12i 441 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
anbi12.1 (𝜑𝜓)
anbi12.2 (𝜒𝜃)
Assertion
Ref Expression
anbi12ci ((𝜑𝜒) ↔ (𝜃𝜓))

Proof of Theorem anbi12ci
StepHypRef Expression
1 anbi12.1 . . 3 (𝜑𝜓)
2 anbi12.2 . . 3 (𝜒𝜃)
31, 2anbi12i 441 . 2 ((𝜑𝜒) ↔ (𝜓𝜃))
4 ancom 257 . 2 ((𝜓𝜃) ↔ (𝜃𝜓))
53, 4bitri 177 1 ((𝜑𝜒) ↔ (𝜃𝜓))
Colors of variables: wff set class
Syntax hints:  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  opelopabsbALT  4023  cnvpom  4887  f1cnvcnv  5127
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