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Theorem ralrimivva 2395
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version with double quantification.) (Contributed by Jeff Madsen, 19-Jun-2011.)
Hypothesis
Ref Expression
ralrimivva.1 ((φ (x A y B)) → ψ)
Assertion
Ref Expression
ralrimivva (φx A y B ψ)
Distinct variable groups:   φ,x,y   y,A
Allowed substitution hints:   ψ(x,y)   A(x)   B(x,y)

Proof of Theorem ralrimivva
StepHypRef Expression
1 ralrimivva.1 . . 3 ((φ (x A y B)) → ψ)
21ex 108 . 2 (φ → ((x A y B) → ψ))
32ralrimivv 2394 1 (φx A y B ψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1390  wral 2300
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 1333  ax-gen 1335  ax-4 1397  ax-17 1416
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305
This theorem is referenced by:  swopo  4034  sosng  4356  fcof1  5366  fliftfund  5380  isoresbr  5392  isocnv  5394  f1oiso  5408  caovclg  5595  caovcomg  5598  off  5666  caofrss  5677  fmpt2co  5779  poxp  5794  eroprf  6135  dom2lem  6188  addlocpr  6518  mullocpr  6551  cauappcvgprlemloc  6623  cauappcvgprlemlim  6632  cju  7674  frec2uzf1od  8853  frec2uzisod  8854  frecuzrdgrrn  8855
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