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Theorem rexlimivw 2522
Description: Weaker version of rexlimiv 2520. (Contributed by FL, 19-Sep-2011.)
Hypothesis
Ref Expression
rexlimivw.1 (𝜑𝜓)
Assertion
Ref Expression
rexlimivw (∃𝑥𝐴 𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimivw
StepHypRef Expression
1 rexlimivw.1 . . 3 (𝜑𝜓)
21a1i 9 . 2 (𝑥𝐴 → (𝜑𝜓))
32rexlimiv 2520 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:  r19.29vva  2554  eliun  3787  reusv3i  4350  elrnmptg  4761  fun11iun  5356  fmpt  5538  fliftfun  5665  elrnmpo  5852  releldm2  6051  tfrlem4  6178  iinerm  6469  elixpsn  6597  isfi  6623  cardcl  7005  cardval3ex  7009  ltbtwnnqq  7191  recexprlemlol  7402  recexprlemupu  7404  suplocsr  7585  restsspw  12057  ssnei  12247  tgcnp  12305  xmetunirn  12454  metss  12590  metrest  12602
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