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Theorem ralrimdvv 2708
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version with double quantification.) (Contributed by NM, 1-Jun-2005.)
Hypothesis
Ref Expression
ralrimdvv.1 (φ → (ψ → ((x A y B) → χ)))
Assertion
Ref Expression
ralrimdvv (φ → (ψx A y B 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 ralrimdvv
StepHypRef Expression
1 ralrimdvv.1 . . . 4 (φ → (ψ → ((x A y B) → χ)))
21imp 418 . . 3 ((φ ψ) → ((x A y B) → χ))
32ralrimivv 2705 . 2 ((φ ψ) → x A y B χ)
43ex 423 1 (φ → (ψx A y B χ))
 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:  ralrimdvva  2709
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