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Theorem rexlimivv 2743
 Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 17-Feb-2004.)
Hypothesis
Ref Expression
rexlimivv.1 ((x A y B) → (φψ))
Assertion
Ref Expression
rexlimivv (x A y B φψ)
Distinct variable groups:   x,y,ψ   y,A
Allowed substitution hints:   φ(x,y)   A(x)   B(x,y)

Proof of Theorem rexlimivv
StepHypRef Expression
1 rexlimivv.1 . . 3 ((x A y B) → (φψ))
21rexlimdva 2738 . 2 (x A → (y B φψ))
32rexlimiv 2732 1 (x A y B φψ)
 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:  2reu5  3044  tfin11  4493  peano4nc  6150  sbth  6206  nclenc  6222  lenc  6223  letc  6231  ce2le  6233
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