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Theorem rspcedvd 2822
 Description: Restricted existential specialization, using implicit substitution. Variant of rspcedv 2820. (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 2820 . 2
51, 4mpd 13 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1335   wcel 2128  wrex 2436 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-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-v 2714 This theorem is referenced by:  rspcime  2823  rspcedeq1vd  2825  rspcedeq2vd  2826  updjud  7016  elpq  9539  modqmuladd  10247  modqmuladdnn0  10249  modfzo0difsn  10276  negfi  11109  divconjdvds  11722  2tp1odd  11756  dfgcd2  11878  qredeu  11954  pw2dvdslemn  12019  xmettx  12870  bj-charfunbi  13346
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