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Theorem anim12dan 600
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 115 . . 3 (𝜑 → (𝜓𝜒))
3 anim12dan.2 . . . 4 ((𝜑𝜃) → 𝜏)
43ex 115 . . 3 (𝜑 → (𝜃𝜏))
52, 4anim12d 335 . 2 (𝜑 → ((𝜓𝜃) → (𝜒𝜏)))
65imp 124 1 ((𝜑 ∧ (𝜓𝜃)) → (𝜒𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  xpexr2m  5065  isocnv  5805  f1oiso  5820  f1oiso2  5821  f1o2ndf1  6222  xpf1o  6837  pc11  12300  mhmpropd  12734  tgclb  13198  innei  13296  txcn  13408  lgsdir2  14067
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