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Theorem rexlimdvv 2744
 Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Jul-2004.)
Hypothesis
Ref Expression
rexlimdvv.1 (φ → ((x A y B) → (ψχ)))
Assertion
Ref Expression
rexlimdvv (φ → (x A y B ψχ))
Distinct variable groups:   x,y,φ   χ,x,y   y,A
Allowed substitution hints:   ψ(x,y)   A(x)   B(x,y)

Proof of Theorem rexlimdvv
StepHypRef Expression
1 rexlimdvv.1 . . . 4 (φ → ((x A y B) → (ψχ)))
21expdimp 426 . . 3 ((φ x A) → (y B → (ψχ)))
32rexlimdv 2737 . 2 ((φ x A) → (y B ψχ))
43rexlimdva 2738 1 (φ → (x A y B ψχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∃wrex 2615 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-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2619  df-rex 2620 This theorem is referenced by:  rexlimdvva  2745  ncfinraise  4481  ncfinlower  4483  nnpw1ex  4484  nnpweq  4523  sfinltfin  4535  f1oiso2  5500  addcdi  6250
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