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Theorem anim12dan 542
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 112 . . 3 (𝜑 → (𝜓𝜒))
3 anim12dan.2 . . . 4 ((𝜑𝜃) → 𝜏)
43ex 112 . . 3 (𝜑 → (𝜃𝜏))
52, 4anim12d 322 . 2 (𝜑 → ((𝜓𝜃) → (𝜒𝜏)))
65imp 119 1 ((𝜑 ∧ (𝜓𝜃)) → (𝜒𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  xpexr2m  4789  isocnv  5478  f1oiso  5492  f1oiso2  5493  f1o2ndf1  5876
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