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Theorem rexlimdvw 2481
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Jun-2014.)
Hypothesis
Ref Expression
rexlimdvw.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
rexlimdvw  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Distinct variable groups:    ph, x    ch, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem rexlimdvw
StepHypRef Expression
1 rexlimdvw.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21a1d 22 . 2  |-  ( ph  ->  ( x  e.  A  ->  ( ps  ->  ch ) ) )
32rexlimdv 2477 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   E.wrex 2350
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-ral 2354  df-rex 2355
This theorem is referenced by:  qsss  6231  ltpopr  6847  ltsopr  6848  ltexprlemlol  6854  ltexprlemupu  6856  cauappcvgprlemrnd  6902  caucvgprlemrnd  6925  caucvgprprlemrnd  6953  climuni  10270  bj-findis  10932
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