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Theorem anim12dan 532
 Description: Conjoin antecedents and consequents in a deduction. (Contributed by Mario Carneiro, 12-May-2014.)
Hypotheses
Ref Expression
anim12dan.1 ((𝜑𝜓) → 𝜒)
anim12dan.2 ((𝜑𝜃) → 𝜏)
Assertion
Ref Expression
anim12dan ((𝜑 ∧ (𝜓𝜃)) → (𝜒𝜏))

Proof of Theorem anim12dan
StepHypRef Expression
1 anim12dan.1 . . . 4 ((𝜑𝜓) → 𝜒)
21ex 108 . . 3 (𝜑 → (𝜓𝜒))
3 anim12dan.2 . . . 4 ((𝜑𝜃) → 𝜏)
43ex 108 . . 3 (𝜑 → (𝜃𝜏))
52, 4anim12d 318 . 2 (𝜑 → ((𝜓𝜃) → (𝜒𝜏)))
65imp 115 1 ((𝜑 ∧ (𝜓𝜃)) → (𝜒𝜏))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97 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 This theorem is referenced by:  xpexr2m  4762  isocnv  5451  f1oiso  5465  f1oiso2  5466  f1o2ndf1  5849
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