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

Theorem ralrimdvva 2709
 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 (x A y B)) → (ψχ))
Assertion
Ref Expression
ralrimdvva (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 ralrimdvva
StepHypRef Expression
1 ralrimdvva.1 . . . 4 ((φ (x A y B)) → (ψχ))
21ex 423 . . 3 (φ → ((x A y B) → (ψχ)))
32com23 72 . 2 (φ → (ψ → ((x A y B) → χ)))
43ralrimdvv 2708 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-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: (None)
 Copyright terms: Public domain W3C validator