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Theorem alimd 2245
Description: Deduction form of Theorem 19.20 of [Margaris] p. 90, see alim 1905. (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 2227 . 2 (𝜑 → ∀𝑥𝜑)
3 alimd.2 . 2 (𝜑 → (𝜓𝜒))
42, 3alimdh 1912 1 (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1650  wnf 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-12 2211
This theorem depends on definitions:  df-bi 198  df-ex 1875  df-nf 1879
This theorem is referenced by:  alrimdd  2247  nfald  2331  mo3  2628  2mo  2673  axpowndlem3  9674  axext4dist  32149  bj-mo3OLD  33261  pm11.71  39271
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