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Theorem rexlimiv 2520
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994.)
Hypothesis
Ref Expression
rexlimiv.1 (𝑥𝐴 → (𝜑𝜓))
Assertion
Ref Expression
rexlimiv (∃𝑥𝐴 𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimiv
StepHypRef Expression
1 nfv 1493 . 2 𝑥𝜓
2 rexlimiv.1 . 2 (𝑥𝐴 → (𝜑𝜓))
31, 2rexlimi 2519 1 (∃𝑥𝐴 𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1465  wrex 2394
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-ral 2398  df-rex 2399
This theorem is referenced by:  rexlimiva  2521  rexlimivw  2522  rexlimivv  2532  r19.36av  2559  r19.44av  2567  r19.45av  2568  rexn0  3431  uniss2  3737  elres  4825  ssimaex  5450  tfrlem5  6179  tfrlem8  6183  ecoptocl  6484  mapsn  6552  elixpsn  6597  ixpsnf1o  6598  findcard  6750  findcard2  6751  findcard2s  6752  fiintim  6785  prnmaddl  7266  0re  7734  cnegexlem2  7906  0cnALT  7920  bndndx  8944  uzn0  9309  ublbneg  9373  rexanuz2  10731  opnneiid  12260  bj-inf2vnlem2  13096
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