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Theorem reximdvai 2462
Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 14-Nov-2002.)
Hypothesis
Ref Expression
reximdvai.1  |-  ( ph  ->  ( x  e.  A  ->  ( ps  ->  ch ) ) )
Assertion
Ref Expression
reximdvai  |-  ( ph  ->  ( E. x  e.  A  ps  ->  E. x  e.  A  ch )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)    A( x)

Proof of Theorem reximdvai
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ x ph
2 reximdvai.1 . 2  |-  ( ph  ->  ( x  e.  A  ->  ( ps  ->  ch ) ) )
31, 2reximdai 2460 1  |-  ( ph  ->  ( E. x  e.  A  ps  ->  E. x  e.  A  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   E.wrex 2350
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-ral 2354  df-rex 2355
This theorem is referenced by:  reximdv  2463  reximdva  2464  reuind  2796
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