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Theorem ralrimdvva 2957
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version with double quantification.) (Contributed by NM, 2-Feb-2008.)
Hypothesis
Ref Expression
ralrimdvva.1 ((𝜑 ∧ (𝑥𝐴𝑦𝐵)) → (𝜓𝜒))
Assertion
Ref Expression
ralrimdvva (𝜑 → (𝜓 → ∀𝑥𝐴𝑦𝐵 𝜒))
Distinct variable groups:   𝑥,𝑦,𝜑   𝜓,𝑥,𝑦   𝑦,𝐴
Allowed substitution hints:   𝜒(𝑥,𝑦)   𝐴(𝑥)   𝐵(𝑥,𝑦)

Proof of Theorem ralrimdvva
StepHypRef Expression
1 ralrimdvva.1 . . . 4 ((𝜑 ∧ (𝑥𝐴𝑦𝐵)) → (𝜓𝜒))
21ex 449 . . 3 (𝜑 → ((𝑥𝐴𝑦𝐵) → (𝜓𝜒)))
32com23 84 . 2 (𝜑 → (𝜓 → ((𝑥𝐴𝑦𝐵) → 𝜒)))
43ralrimdvv 2956 1 (𝜑 → (𝜓 → ∀𝑥𝐴𝑦𝐵 𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∈ wcel 1977  ∀wral 2896 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 This theorem depends on definitions:  df-bi 196  df-an 385  df-ral 2901 This theorem is referenced by:  isosolem  6497  kgencn2  21170  fbunfip  21483  reconn  22439  c1lip1  23564  cdj3i  28684  poimirlem29  32608  ispridl2  33007  ispridlc  33039
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