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Theorem ralrimdvva 3199
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 413 . . 3 (𝜑 → ((𝑥𝐴𝑦𝐵) → (𝜓𝜒)))
32com23 86 . 2 (𝜑 → (𝜓 → ((𝑥𝐴𝑦𝐵) → 𝜒)))
43ralrimdvv 3198 1 (𝜑 → (𝜓 → ∀𝑥𝐴𝑦𝐵 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wcel 2107  wral 3143
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904
This theorem depends on definitions:  df-bi 208  df-an 397  df-ral 3148
This theorem is referenced by:  isosolem  7092  kgencn2  22081  fbunfip  22393  reconn  23351  c1lip1  24509  cdj3i  30132  poimirlem29  34788  ispridl2  35184  ispridlc  35216
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