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Theorem anim12ii 335
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 270 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 anim12ii.2 . . 3 (𝜃 → (𝜓𝜏))
43adantl 271 . 2 ((𝜑𝜃) → (𝜓𝜏))
52, 4jcad 301 1 ((𝜑𝜃) → (𝜓 → (𝜒𝜏)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem is referenced by:  euim  2010  elex22  2615  tz7.2  4111  funcnvuni  4993  bj-findis  10917
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