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Theorem ralrimdv 2556
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 27-May-1998.)
Hypothesis
Ref Expression
ralrimdv.1  |-  ( ph  ->  ( ps  ->  (
x  e.  A  ->  ch ) ) )
Assertion
Ref Expression
ralrimdv  |-  ( ph  ->  ( ps  ->  A. x  e.  A  ch )
)
Distinct variable groups:    ph, x    ps, x
Allowed substitution hints:    ch( x)    A( x)

Proof of Theorem ralrimdv
StepHypRef Expression
1 nfv 1528 . 2  |-  F/ x ph
2 nfv 1528 . 2  |-  F/ x ps
3 ralrimdv.1 . 2  |-  ( ph  ->  ( ps  ->  (
x  e.  A  ->  ch ) ) )
41, 2, 3ralrimd 2555 1  |-  ( ph  ->  ( ps  ->  A. x  e.  A  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2148   A.wral 2455
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-4 1510  ax-17 1526
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-ral 2460
This theorem is referenced by:  ralrimdva  2557  ralrimivv  2558  nneneq  6856  fzrevral  10102  topbas  13460  neipsm  13547  cnpnei  13612  metcnp3  13904
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