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Theorem spcimedv 2706
 Description: Restricted existential specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypotheses
Ref Expression
spcimdv.1
spcimedv.2
Assertion
Ref Expression
spcimedv
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem spcimedv
StepHypRef Expression
1 spcimedv.2 . . . 4
21ex 114 . . 3
32alrimiv 1803 . 2
4 spcimdv.1 . 2
5 nfv 1467 . . 3
6 nfcv 2229 . . 3
75, 6spcimegft 2698 . 2
83, 4, 7sylc 62 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1288   wceq 1290  wex 1427   wcel 1439 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622 This theorem is referenced by:  rspcimedv  2725  fihashf1rn  10258
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