New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  ralrimivv GIF version

Theorem ralrimivv 2705
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version with double quantification.) (Contributed by NM, 24-Jul-2004.)
Hypothesis
Ref Expression
ralrimivv.1 (φ → ((x A y B) → ψ))
Assertion
Ref Expression
ralrimivv (φx A y B ψ)
Distinct variable groups:   x,y,φ   y,A
Allowed substitution hints:   ψ(x,y)   A(x)   B(x,y)

Proof of Theorem ralrimivv
StepHypRef Expression
1 ralrimivv.1 . . . 4 (φ → ((x A y B) → ψ))
21exp3a 425 . . 3 (φ → (x A → (y Bψ)))
32ralrimdv 2703 . 2 (φ → (x Ay B ψ))
43ralrimiv 2696 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-mp 5  ax-1 6  ax-2 7  ax-3 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:  ralrimivva  2706  ralrimdvv  2708  reuind  3039  nnpweq  4523  trrd  5925  connexrd  5930
 Copyright terms: Public domain W3C validator