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Theorem anbi2ci 447
Description: Variant of anbi2i 445 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Hypothesis
Ref Expression
bi.aa (𝜑𝜓)
Assertion
Ref Expression
anbi2ci ((𝜑𝜒) ↔ (𝜒𝜓))

Proof of Theorem anbi2ci
StepHypRef Expression
1 bi.aa . . 3 (𝜑𝜓)
21anbi1i 446 . 2 ((𝜑𝜒) ↔ (𝜓𝜒))
3 ancom 262 . 2 ((𝜓𝜒) ↔ (𝜒𝜓))
42, 3bitri 182 1 ((𝜑𝜒) ↔ (𝜒𝜓))
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:  clabel  2208  ordpwsucss  4338  asymref  4760  supmoti  6500
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