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Theorem alanimi 1470
Description: Variant of al2imi 1469 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 115 . . 3 (𝜑 → (𝜓𝜒))
32al2imi 1469 . 2 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
43imp 124 1 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ∀𝑥𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wal 1362
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460
This theorem is referenced by:  19.26  1492  alsyl  1646  vtoclgft  2802  euind  2939  reuind  2957  sbeqalb  3034  bm1.3ii  4139  trin2  5038  bdbm1.3ii  15101
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