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Theorem reximssdv 2539
 Description: Derivation of a restricted existential quantification over a subset (the second hypothesis implies ), deduction form. (Contributed by AV, 21-Aug-2022.)
Hypotheses
Ref Expression
reximssdv.1
reximssdv.2
reximssdv.3
Assertion
Ref Expression
reximssdv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem reximssdv
StepHypRef Expression
1 reximssdv.1 . 2
2 reximssdv.2 . . . . 5
3 reximssdv.3 . . . . 5
42, 3jca 304 . . . 4
54ex 114 . . 3
65reximdv2 2534 . 2
71, 6mpd 13 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wcel 1481  wrex 2418 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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515 This theorem depends on definitions:  df-bi 116  df-rex 2423 This theorem is referenced by:  suplocexprlemrl  7548  neissex  12371  iscnp4  12424  suplociccex  12809
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