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Theorem al2imi 1363
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 1360 . 2 (∀𝑥𝜑 → ∀𝑥(𝜓𝜒))
3 alim 1362 . 2 (∀𝑥(𝜓𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
42, 3syl 14 1 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1352  ax-gen 1354
This theorem is referenced by:  alanimi  1364  alimdh  1372  albi  1373  19.30dc  1534  19.33b2  1536  hbnt  1559  ax10o  1619  spimth  1639  sbi1v  1787  ralim  2397  ceqsalt  2597  intss  3664
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