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Theorem al2im 1889
Description: Closed form of al2imi 1890. Version of alim 1885 for a nested implication. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
al2im (∀𝑥(𝜑 → (𝜓𝜒)) → (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒)))

Proof of Theorem al2im
StepHypRef Expression
1 alim 1885 . 2 (∀𝑥(𝜑 → (𝜓𝜒)) → (∀𝑥𝜑 → ∀𝑥(𝜓𝜒)))
2 alim 1885 . 2 (∀𝑥(𝜓𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
31, 2syl6 35 1 (∀𝑥(𝜑 → (𝜓𝜒)) → (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1884
This theorem is referenced by:  al2imi  1890  bj-alanim  32927  al3im  38457  19.41rgVD  39654
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