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Theorem anim12d1 612
Description: Variant of anim12d 611 where the second implication does not depend on the antecedent. (Contributed by Rodolfo Medina, 12-Oct-2010.)
Hypotheses
Ref Expression
anim12d1.1 (𝜑 → (𝜓𝜒))
anim12d1.2 (𝜃𝜏)
Assertion
Ref Expression
anim12d1 (𝜑 → ((𝜓𝜃) → (𝜒𝜏)))

Proof of Theorem anim12d1
StepHypRef Expression
1 anim12d1.1 . 2 (𝜑 → (𝜓𝜒))
2 anim12d1.2 . . 3 (𝜃𝜏)
32a1i 11 . 2 (𝜑 → (𝜃𝜏))
41, 3anim12d 611 1 (𝜑 → ((𝜓𝜃) → (𝜒𝜏)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399
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 210  df-an 400
This theorem is referenced by:  fun  6530  alephord  9499  grudomon  10237  xrsupexmnf  12695  xrinfmexpnf  12696  joinfval  17611  meetfval  17625  cnpresti  21900  1stcrest  22065  upgrwlkdvdelem  27532  frrlem13  33196
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