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Theorem 3anim1i 1138
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 ((φ χ θ) → (ψ χ θ))

Proof of Theorem 3anim1i
StepHypRef Expression
1 3animi.1 . 2 (φψ)
2 id 19 . 2 (χχ)
3 id 19 . 2 (θθ)
41, 2, 33anim123i 1137 1 ((φ χ θ) → (ψ χ θ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   w3a 934
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 177  df-an 360  df-3an 936
This theorem is referenced by:  syl3an1  1215  syl3anl1  1230  syl3anr1  1234
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