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Theorem ralrimdva 2399
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 2-Feb-2008.)
Hypothesis
Ref Expression
ralrimdva.1 ((𝜑𝑥𝐴) → (𝜓𝜒))
Assertion
Ref Expression
ralrimdva (𝜑 → (𝜓 → ∀𝑥𝐴 𝜒))
Distinct variable groups:   𝜑,𝑥   𝜓,𝑥
Allowed substitution hints:   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem ralrimdva
StepHypRef Expression
1 ralrimdva.1 . . . 4 ((𝜑𝑥𝐴) → (𝜓𝜒))
21ex 108 . . 3 (𝜑 → (𝑥𝐴 → (𝜓𝜒)))
32com23 72 . 2 (𝜑 → (𝜓 → (𝑥𝐴𝜒)))
43ralrimdv 2398 1 (𝜑 → (𝜓 → ∀𝑥𝐴 𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∈ wcel 1393  ∀wral 2306 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-ral 2311 This theorem is referenced by:  ralxfrd  4194  isoselem  5459  isosolem  5463  findcard  6345  nnsub  7952  ublbneg  8548  expnlbnd2  9374  cau3lem  9710  climshftlemg  9823  subcn2  9832  serif0  9871  sqrt2irr  9878
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