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Theorem rexlimiv 2421
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 1418 . 2 xψ
2 rexlimiv.1 . 2 (x A → (φψ))
31, 2rexlimi 2420 1 (x A φψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  wrex 2301
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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305  df-rex 2306
This theorem is referenced by:  rexlimiva  2422  rexlimivw  2423  rexlimivv  2432  r19.36av  2455  r19.44av  2463  r19.45av  2464  rexn0  3313  uniss2  3602  elres  4589  ssimaex  5177  tfrlem5  5871  tfrlem8  5875  ecoptocl  6129  prnmaddl  6472  0re  6785  cnegexlem2  6944  0cnALT  6958  bndndx  7916  uzn0  8224  ublbneg  8284  bj-inf2vnlem2  9355
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