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Theorem 3anim1i 1090
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 1089 1 ((𝜑𝜒𝜃) → (𝜓𝜒𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  syl3an1  1168  syl3anl1  1183  syl3anr1  1187  elioc2  8805  elico2  8806  elicc2  8807
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