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Theorem al2imi 1438
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 1435 . 2 (∀𝑥𝜑 → ∀𝑥(𝜓𝜒))
3 alim 1437 . 2 (∀𝑥(𝜓𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
42, 3syl 14 1 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1333
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1427  ax-gen 1429
This theorem is referenced by:  alanimi  1439  alimdh  1447  albi  1448  19.30dc  1607  19.33b2  1609  hbnt  1633  ax10o  1695  spimth  1715  sbi1v  1871  ralim  2516  ceqsalt  2738  intss  3830
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