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Theorem alimdh 1734
Description: Deduction form of Theorem 19.20 of [Margaris] p. 90, see alim 1728. (Contributed by NM, 4-Jan-2002.)
Hypotheses
Ref Expression
alimdh.1 (𝜑 → ∀𝑥𝜑)
alimdh.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alimdh (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Proof of Theorem alimdh
StepHypRef Expression
1 alimdh.1 . 2 (𝜑 → ∀𝑥𝜑)
2 alimdh.2 . . 3 (𝜑 → (𝜓𝜒))
32al2imi 1732 . 2 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
41, 3syl 17 1 (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1712  ax-4 1727
This theorem is referenced by:  alrimdh  1776  alimdv  1831  hbald  2026  alimd  2066  alimdOLD  2177  dral1-o  33010  ax12indalem  33051  ax12inda2ALT  33052
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