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Theorem rexlimdvw 2578
 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 2573 1 (𝜑 → (∃𝑥𝐴 𝜓𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 2128  ∃wrex 2436 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 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-17 1506  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-ral 2440  df-rex 2441 This theorem is referenced by:  nnpredcl  4580  qsss  6532  fodjuomnilemdc  7070  ltpopr  7498  ltsopr  7499  ltexprlemlol  7505  ltexprlemupu  7507  cauappcvgprlemrnd  7553  caucvgprlemrnd  7576  caucvgprprlemrnd  7604  suplocexprlemss  7618  suplocexprlemrl  7620  suplocsrlempr  7710  climuni  11172  cncnp2m  12591  bj-findis  13513
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