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Theorem rexlimdvw 2553
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 2548 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1480   E.wrex 2417
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-ral 2421  df-rex 2422
This theorem is referenced by:  nnpredcl  4536  qsss  6488  fodjuomnilemdc  7016  ltpopr  7410  ltsopr  7411  ltexprlemlol  7417  ltexprlemupu  7419  cauappcvgprlemrnd  7465  caucvgprlemrnd  7488  caucvgprprlemrnd  7516  suplocexprlemss  7530  suplocexprlemrl  7532  suplocsrlempr  7622  climuni  11069  cncnp2m  12410  bj-findis  13207
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