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Theorem rspcedvd 2709
 Description: Restricted existential specialization, using implicit substitution. Variant of rspcedv 2706. (Contributed by AV, 27-Nov-2019.)
Hypotheses
Ref Expression
rspcedvd.1
rspcedvd.2
rspcedvd.3
Assertion
Ref Expression
rspcedvd
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rspcedvd
StepHypRef Expression
1 rspcedvd.3 . 2
2 rspcedvd.1 . . 3
3 rspcedvd.2 . . 3
42, 3rspcedv 2706 . 2
51, 4mpd 13 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285   wcel 1434  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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604 This theorem is referenced by:  rspcedeq1vd  2710  rspcedeq2vd  2711  modqmuladd  9448  modqmuladdnn0  9450  modfzo0difsn  9477  negfi  10248  divconjdvds  10394  2tp1odd  10428  dfgcd2  10547  qredeu  10623  pw2dvdslemn  10687
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