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Theorem rexlimiv 2405
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994.)
Hypothesis
Ref Expression
rexlimiv.1 (x A → (φψ))
Assertion
Ref Expression
rexlimiv (x A φψ)
Distinct variable group:   ψ,x
Allowed substitution hints:   φ(x)   A(x)

Proof of Theorem rexlimiv
StepHypRef Expression
1 nfv 1402 . 2 xψ
2 rexlimiv.1 . 2 (x A → (φψ))
31, 2rexlimi 2404 1 (x A φψ)
Colors of variables: wff set class
Syntax hints:  wi 4   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:  rexlimiva  2406  rexlimivw  2407  rexlimivv  2416  r19.36av  2439  r19.44av  2447  r19.45av  2448  rexn0  3298  uniss2  3585  elres  4573  ssimaex  5159  tfrlem5  5852  tfrlem8  5856  ecoptocl  6104  prnmaddl  6344  0re  6629  cnegexlem2  6774  0cnALT  6788  bj-inf2vnlem2  7189
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