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Theorem anim12ci 337
Description: Variant of anim12i 336 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 336 . 2 ((𝜒𝜑) → (𝜃𝜓))
43ancoms 266 1 ((𝜑𝜒) → (𝜃𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  anim1ci  339  dfco2a  5043  funco  5167  fliftval  5705  ltsrprg  7575  difelfznle  9939  iseqf1olemqk  10294  ex-ceil  13092
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