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Theorem 3anim1i 1168
Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.)
Hypothesis
Ref Expression
3animi.1 (𝜑𝜓)
Assertion
Ref Expression
3anim1i ((𝜑𝜒𝜃) → (𝜓𝜒𝜃))

Proof of Theorem 3anim1i
StepHypRef Expression
1 3animi.1 . 2 (𝜑𝜓)
2 id 19 . 2 (𝜒𝜒)
3 id 19 . 2 (𝜃𝜃)
41, 2, 33anim123i 1167 1 ((𝜑𝜒𝜃) → (𝜓𝜒𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  syl3an1  1250  syl3anl1  1265  syl3anr1  1269  elioc2  9749  elico2  9750  elicc2  9751  dvdsleabs2  11580
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