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Theorem rexlimiva 2521
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Dec-2006.)
Hypothesis
Ref Expression
rexlimiva.1 ((𝑥𝐴𝜑) → 𝜓)
Assertion
Ref Expression
rexlimiva (∃𝑥𝐴 𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimiva
StepHypRef Expression
1 rexlimiva.1 . . 3 ((𝑥𝐴𝜑) → 𝜓)
21ex 114 . 2 (𝑥𝐴 → (𝜑𝜓))
32rexlimiv 2520 1 (∃𝑥𝐴 𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  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:  unon  4397  reg2exmidlema  4419  ssfilem  6737  diffitest  6749  fival  6826  elfi2  6828  fi0  6831  djuss  6923  updjud  6935  enumct  6968  finnum  7007  dmaddpqlem  7153  nqpi  7154  nq0nn  7218  recexprlemm  7400  rexanuz  10728  r19.2uz  10733  maxleast  10953  fsum2dlemstep  11171  fisumcom2  11175  0dvds  11440  even2n  11498  m1expe  11523  m1exp1  11525  epttop  12186  neipsm  12250  tgioo  12642  sin0pilem2  12790  pilem3  12791  bj-nn0suc  13089  bj-nn0sucALT  13103
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