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Theorem alanimi 1810
Description: Variant of al2imi 1809 with conjunctive antecedent. (Contributed by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
alanimi.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
alanimi ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ∀𝑥𝜒)

Proof of Theorem alanimi
StepHypRef Expression
1 alanimi.1 . . . 4 ((𝜑𝜓) → 𝜒)
21ex 415 . . 3 (𝜑 → (𝜓𝜒))
32al2imi 1809 . 2 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
43imp 409 1 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ∀𝑥𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  wal 1528
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803
This theorem depends on definitions:  df-bi 209  df-an 399
This theorem is referenced by:  19.26  1864  alsyl  1887  ax13  2386  nfeqf  2392  darapti  2765  axextmo  2795  vtoclgft  3552  vtoclgftOLD  3553  euind  3713  reuind  3742  sbeqalb  3834  bm1.3ii  5197  trin2  5976  bj-nnfan  34065  bj-cbv3ta  34096  bj-bm1.3ii  34344  mpobi123f  35427  mptbi12f  35431  cotrintab  39959  albitr  40680  2alanimi  40689
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