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Theorem al2imi 1451
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 1448 . 2 (∀𝑥𝜑 → ∀𝑥(𝜓𝜒))
3 alim 1450 . 2 (∀𝑥(𝜓𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
42, 3syl 14 1 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1346
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1440  ax-gen 1442
This theorem is referenced by:  alanimi  1452  alimdh  1460  albi  1461  19.30dc  1620  19.33b2  1622  hbnt  1646  ax10o  1708  spimth  1728  sbi1v  1884  ralim  2529  ceqsalt  2756  intss  3852
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