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Theorem anim12ci 326
Description: Variant of anim12i 325 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
anim12i.1 (𝜑𝜓)
anim12i.2 (𝜒𝜃)
Assertion
Ref Expression
anim12ci ((𝜑𝜒) → (𝜃𝜓))

Proof of Theorem anim12ci
StepHypRef Expression
1 anim12i.2 . . 3 (𝜒𝜃)
2 anim12i.1 . . 3 (𝜑𝜓)
31, 2anim12i 325 . 2 ((𝜒𝜑) → (𝜃𝜓))
43ancoms 259 1 ((𝜑𝜒) → (𝜃𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem is referenced by:  dfco2a  4848  funco  4967  fliftval  5467  ltsrprg  6889  difelfznle  9094  ex-ceil  10259
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