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Theorem ralrimivva 2706
 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 423 . 2 (φ → ((x A y B) → ψ))
32ralrimivv 2705 1 (φx A y B ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∀wral 2614 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by:  nnpw1ex  4484  isocnv  5491  isotr  5495  f1oiso  5499  caovcld  5622  caovcomg  5624  antird  5928  iserd  5942  ncspw1eu  6159
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