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Theorem anbi2ci 677
Description: Variant of anbi2i 675 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 ((φ χ) ↔ (χ ψ))

Proof of Theorem anbi2ci
StepHypRef Expression
1 bi.aa . . 3 (φψ)
21anbi1i 676 . 2 ((φ χ) ↔ (ψ χ))
3 ancom 437 . 2 ((ψ χ) ↔ (χ ψ))
42, 3bitri 240 1 ((φ χ) ↔ (χ ψ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  clabel  2474  enmap2lem1  6063  enmap1lem1  6069  lecex  6115
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