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Theorem anim12ii 620
Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 11-Nov-2007.) (Proof shortened by Wolf Lammen, 19-Jul-2013.)
Hypotheses
Ref Expression
anim12ii.1 (𝜑 → (𝜓𝜒))
anim12ii.2 (𝜃 → (𝜓𝜏))
Assertion
Ref Expression
anim12ii ((𝜑𝜃) → (𝜓 → (𝜒𝜏)))

Proof of Theorem anim12ii
StepHypRef Expression
1 anim12ii.1 . 2 (𝜑 → (𝜓𝜒))
2 anim12ii.2 . 2 (𝜃 → (𝜓𝜏))
3 pm3.43 477 . 2 (((𝜓𝜒) ∧ (𝜓𝜏)) → (𝜓 → (𝜒𝜏)))
41, 2, 3syl2an 598 1 ((𝜑𝜃) → (𝜓 → (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:  im2anan9  622  pm5.31r  830  euimOLD  2705  2mo  2736  elex22  3502  tz7.2  5520  funcnvuni  7619  upgrwlkdvdelem  27514  funressnfv  43477
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