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Theorem rexlimdvw 2530
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Jun-2014.)
Hypothesis
Ref Expression
rexlimdvw.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
rexlimdvw (𝜑 → (∃𝑥𝐴 𝜓𝜒))
Distinct variable groups:   𝜑,𝑥   𝜒,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimdvw
StepHypRef Expression
1 rexlimdvw.1 . . 3 (𝜑 → (𝜓𝜒))
21a1d 22 . 2 (𝜑 → (𝑥𝐴 → (𝜓𝜒)))
32rexlimdv 2525 1 (𝜑 → (∃𝑥𝐴 𝜓𝜒))
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:  nnpredcl  4506  qsss  6456  fodjuomnilemdc  6984  ltpopr  7371  ltsopr  7372  ltexprlemlol  7378  ltexprlemupu  7380  cauappcvgprlemrnd  7426  caucvgprlemrnd  7449  caucvgprprlemrnd  7477  suplocexprlemss  7491  suplocexprlemrl  7493  suplocsrlempr  7583  climuni  11030  cncnp2m  12327  bj-findis  13104
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