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Theorem anbi12ci 434
Description: Variant of anbi12i 433 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 433 . 2 ((φ χ) ↔ (ψ θ))
4 ancom 253 . 2 ((ψ θ) ↔ (θ ψ))
53, 4bitri 173 1 ((φ χ) ↔ (θ ψ))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  opelopabsbALT  3987  cnvpom  4803  f1cnvcnv  5043
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