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Theorem anbi12ci 679
Description: Variant of anbi12i 678 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
anbi12.1 (φψ)
anbi12.2 (χθ)
Assertion
Ref Expression
anbi12ci ((φ χ) ↔ (θ ψ))

Proof of Theorem anbi12ci
StepHypRef Expression
1 anbi12.1 . . 3 (φψ)
2 anbi12.2 . . 3 (χθ)
31, 2anbi12i 678 . 2 ((φ χ) ↔ (ψ θ))
4 ancom 437 . 2 ((ψ θ) ↔ (θ ψ))
53, 4bitri 240 1 ((φ χ) ↔ (θ 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:  funsex  5828  refex  5911  foundex  5914  csucex  6259
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