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Theorem anim12ii 612
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 . . 3 (𝜑 → (𝜓𝜒))
21adantr 473 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 anim12ii.2 . . 3 (𝜃 → (𝜓𝜏))
43adantl 474 . 2 ((𝜑𝜃) → (𝜓𝜏))
52, 4jcad 509 1 ((𝜑𝜃) → (𝜓 → (𝜒𝜏)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385
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 199  df-an 386
This theorem is referenced by:  euim  2678  2mo  2707  elex22  3405  tz7.2  5296  funcnvuni  7354  upgrwlkdvdelem  26990  funressnfv  41926
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