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Theorem ralrimdva 2454
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 114 . . 3 (𝜑 → (𝑥𝐴 → (𝜓𝜒)))
32com23 78 . 2 (𝜑 → (𝜓 → (𝑥𝐴𝜒)))
43ralrimdv 2453 1 (𝜑 → (𝜓 → ∀𝑥𝐴 𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wcel 1439  wral 2360
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-4 1446  ax-17 1465
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-ral 2365
This theorem is referenced by:  ralxfrd  4297  isoselem  5613  isosolem  5617  findcard  6658  nnsub  8522  supinfneg  9144  infsupneg  9145  ublbneg  9159  expnlbnd2  10140  cau3lem  10608  climshftlemg  10751  subcn2  10761  serf0  10802  sqrt2irr  11480
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