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Theorem anim12 808
 Description: Conjoin antecedents and consequents of two premises. This is the closed theorem form of anim12d 611. Theorem *3.47 of [WhiteheadRussell] p. 113. It was proved by Leibniz, and it evidently pleased him enough to call it praeclarum theorema (splendid theorem). (Contributed by NM, 12-Aug-1993.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Assertion
Ref Expression
anim12 (((𝜑𝜓) ∧ (𝜒𝜃)) → ((𝜑𝜒) → (𝜓𝜃)))

Proof of Theorem anim12
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
2 id 22 . 2 ((𝜒𝜃) → (𝜒𝜃))
31, 2im2anan9 622 1 (((𝜑𝜓) ∧ (𝜒𝜃)) → ((𝜑𝜒) → (𝜓𝜃)))
 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:  euind  3640  reuind  3669  reusv3i  5277  opelopabt  5393  wemaplem2  9057  rexanre  14767  rlimcn2  15008  o1of2  15030  o1rlimmul  15036  2sqlem6  26120  spanuni  29440  bj-nnfan  34508  isbasisrelowllem1  35087  isbasisrelowllem2  35088  heicant  35407  pm11.71  41519
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