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Theorem rexlimdvaa 2550
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by Mario Carneiro, 15-Jun-2016.)
Hypothesis
Ref Expression
rexlimdvaa.1  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
Assertion
Ref Expression
rexlimdvaa  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Distinct variable groups:    ph, x    ch, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem rexlimdvaa
StepHypRef Expression
1 rexlimdvaa.1 . . 3  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
21expr 372 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps  ->  ch ) )
32rexlimdva 2549 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    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:  rexlimddv  2554  nnsucuniel  6391  omp1eomlem  6979  ctmlemr  6993  mulgt0sr  7586  axpre-suploclemres  7709  cnegex  7940  receuap  8430  rexanuz  10760  climcaucn  11120  fsumiun  11246  dvdsval2  11496  prmind2  11801  tgcl  12233  neiint  12314  restopnb  12350  iscnp4  12387  blssexps  12598  blssex  12599
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