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Theorem rexlimdvw 2453
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 2449 1 (𝜑 → (∃𝑥𝐴 𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1409  wrex 2324
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-ral 2328  df-rex 2329
This theorem is referenced by:  qsss  6196  ltpopr  6751  ltsopr  6752  ltexprlemlol  6758  ltexprlemupu  6760  cauappcvgprlemrnd  6806  caucvgprlemrnd  6829  caucvgprprlemrnd  6857  climuni  10045  bj-findis  10491
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