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Theorem alanimi 1784
Description: Variant of al2imi 1783 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 1783 . 2 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
43imp 444 1 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ∀𝑥𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wal 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777
This theorem depends on definitions:  df-bi 197  df-an 385
This theorem is referenced by:  19.26  1838  alsyl  1860  ax13  2285  nfeqf  2337  bm1.1  2636  vtoclgft  3285  vtoclgftOLD  3286  euind  3426  reuind  3444  sbeqalb  3521  bm1.3ii  4817  trin2  5554  bj-cbv3ta  32835  mpt2bi123f  34101  mptbi12f  34105  cotrintab  38238  albitr  38879  2alanimi  38888
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