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Theorem rexlimdvaa 2630
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 601 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps  ->  ch ) )
32rexlimdva 2629 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360    e. wcel 1621   E.wrex 2510
This theorem is referenced by:  rexlimddv  2633  sscpwex  13536
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540  df-ral 2513  df-rex 2514
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