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Theorem alanimi 1818
Description: Variant of al2imi 1817 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 413 . . 3 (𝜑 → (𝜓𝜒))
32al2imi 1817 . 2 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
43imp 407 1 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ∀𝑥𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wal 1539
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811
This theorem depends on definitions:  df-bi 206  df-an 397
This theorem is referenced by:  19.26  1873  alsyl  1896  ax13  2374  nfeqf  2380  darapti  2679  axextmo  2707  vtoclgft  3540  euind  3720  reuind  3749  sbeqalb  3845  bm1.3ii  5302  trin2  6124  ssfi  9172  bj-nnfan  35621  bj-cbv3ta  35659  bj-bm1.3ii  35940  mpobi123f  37025  mptbi12f  37029  cotrintab  42355  albitr  43112  2alanimi  43121  ichan  46113
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