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Theorem alanimi 1893
Description: Variant of al2imi 1892 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 449 . . 3 (𝜑 → (𝜓𝜒))
32al2imi 1892 . 2 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
43imp 444 1 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ∀𝑥𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wal 1630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886
This theorem depends on definitions:  df-bi 197  df-an 385
This theorem is referenced by:  19.26  1947  alsyl  1969  ax13  2394  nfeqf  2446  bm1.1  2745  vtoclgft  3394  vtoclgftOLD  3395  euind  3534  reuind  3552  sbeqalb  3629  bm1.3ii  4936  trin2  5677  bj-cbv3ta  33038  mpt2bi123f  34302  mptbi12f  34306  cotrintab  38441  albitr  39082  2alanimi  39091
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