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Theorem rexlimiv 2543
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 1508 . 2 𝑥𝜓
2 rexlimiv.1 . 2 (𝑥𝐴 → (𝜑𝜓))
31, 2rexlimi 2542 1 (∃𝑥𝐴 𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1480  wrex 2417
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-ral 2421  df-rex 2422
This theorem is referenced by:  rexlimiva  2544  rexlimivw  2545  rexlimivv  2555  r19.36av  2582  r19.44av  2590  r19.45av  2591  rexn0  3461  uniss2  3767  elres  4855  ssimaex  5482  tfrlem5  6211  tfrlem8  6215  ecoptocl  6516  mapsn  6584  elixpsn  6629  ixpsnf1o  6630  findcard  6782  findcard2  6783  findcard2s  6784  fiintim  6817  prnmaddl  7310  0re  7778  cnegexlem2  7950  0cnALT  7964  bndndx  8988  uzn0  9353  ublbneg  9417  rexanuz2  10775  opnneiid  12347  bj-inf2vnlem2  13253
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