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Theorem al2imi 1392
Description: Inference quantifying antecedent, nested antecedent, and consequent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
al2imi.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
al2imi (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Proof of Theorem al2imi
StepHypRef Expression
1 al2imi.1 . . 3 (𝜑 → (𝜓𝜒))
21alimi 1389 . 2 (∀𝑥𝜑 → ∀𝑥(𝜓𝜒))
3 alim 1391 . 2 (∀𝑥(𝜓𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
42, 3syl 14 1 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1287
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1381  ax-gen 1383
This theorem is referenced by:  alanimi  1393  alimdh  1401  albi  1402  19.30dc  1563  19.33b2  1565  hbnt  1588  ax10o  1650  spimth  1670  sbi1v  1819  ralim  2434  ceqsalt  2645  intss  3707
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