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Theorem rexlimivv 2416
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 2411 . 2 (x A → (y B φψ))
32rexlimiv 2405 1 (x A y B φψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1374  wrex 2285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-17 1400  ax-ial 1409  ax-i5r 1410
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-ral 2289  df-rex 2290
This theorem is referenced by:  opelxp  4301  f1o2ndf1  5772  distrlem5prl  6425  distrlem5pru  6426  mulid1  6626  cnegex  6782
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