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Theorem alanimi 1436
Description: Variant of al2imi 1435 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 114 . . 3 (𝜑 → (𝜓𝜒))
32al2imi 1435 . 2 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
43imp 123 1 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ∀𝑥𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wal 1330
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426
This theorem is referenced by:  19.26  1458  alsyl  1615  vtoclgft  2739  euind  2874  reuind  2892  sbeqalb  2968  bm1.3ii  4056  trin2  4937  bdbm1.3ii  13258
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