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Theorem alimd 2211
 Description: Deduction form of Theorem 19.20 of [Margaris] p. 90, see alim 1810. See alimdh 1817, alimdv 1916 for variants requiring fewer axioms. (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 2194 . 2 (𝜑 → ∀𝑥𝜑)
3 alimd.2 . 2 (𝜑 → (𝜓𝜒))
42, 3alimdh 1817 1 (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1534  Ⅎwnf 1783 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-12 2176 This theorem depends on definitions:  df-bi 209  df-ex 1780  df-nf 1784 This theorem is referenced by:  alrimdd  2213  nfald  2346  mo3  2647  2mo  2732  axpowndlem3  10024  axextbdist  33049  pm11.71  40735
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