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Theorem anim12ci 322
Description: Variant of anim12i 321 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
anim12i.1 (φψ)
anim12i.2 (χθ)
Assertion
Ref Expression
anim12ci ((φ χ) → (θ ψ))

Proof of Theorem anim12ci
StepHypRef Expression
1 anim12i.2 . . 3 (χθ)
2 anim12i.1 . . 3 (φψ)
31, 2anim12i 321 . 2 ((χ φ) → (θ ψ))
43ancoms 255 1 ((φ χ) → (θ ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
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 is referenced by:  dfco2a  4764  funco  4883  fliftval  5383  ltsrprg  6675  difelfznle  8763
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