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Theorem alimd 2068
 Description: Deduction form of Theorem 19.20 of [Margaris] p. 90, see alim 1729. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alimd.1 𝑥𝜑
alimd.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alimd (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Proof of Theorem alimd
StepHypRef Expression
1 alimd.1 . . 3 𝑥𝜑
21nf5ri 2053 . 2 (𝜑 → ∀𝑥𝜑)
3 alimd.2 . 2 (𝜑 → (𝜓𝜒))
42, 3alimdh 1735 1 (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1473  Ⅎwnf 1699 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701 This theorem is referenced by:  alrimdd  2070  nfald  2151  mo3  2495  2mo  2539  axpowndlem3  9300  axext4dist  30950  bj-mo3OLD  32022  pm11.71  37619
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