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Theorem rexlimdva2 2597
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by Glauco Siliprandi, 2-Jan-2022.)
Hypothesis
Ref Expression
rexlimdva2.1  |-  ( ( ( ph  /\  x  e.  A )  /\  ps )  ->  ch )
Assertion
Ref Expression
rexlimdva2  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Distinct variable groups:    ch, x    ph, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem rexlimdva2
StepHypRef Expression
1 rexlimdva2.1 . . 3  |-  ( ( ( ph  /\  x  e.  A )  /\  ps )  ->  ch )
21exp31 364 . 2  |-  ( ph  ->  ( x  e.  A  ->  ( ps  ->  ch ) ) )
32rexlimdv 2593 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    e. wcel 2148   E.wrex 2456
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-ral 2460  df-rex 2461
This theorem is referenced by:  ctssdclemn0  7102  ctssdc  7105  suplocexprlemru  7696  suplocexprlemloc  7698  suplocsrlemb  7783  ennnfonelemhom  12386  reldvdsrsrg  13073  innei  13296  ivthinclemlr  13748  ivthinclemur  13750  limccnpcntop  13777  limccoap  13780
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