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Theorem rspce 3205
 Description: Restricted existential specialization, using implicit substitution. (Contributed by NM, 26-May-1998.) (Revised by Mario Carneiro, 11-Oct-2016.)
Hypotheses
Ref Expression
rspc.1
rspc.2
Assertion
Ref Expression
rspce
Distinct variable groups:   ,   ,

Proof of Theorem rspce
StepHypRef Expression
1 nfcv 2619 . . . 4
2 nfv 1707 . . . . 5
3 rspc.1 . . . . 5
42, 3nfan 1928 . . . 4
5 eleq1 2529 . . . . 5
6 rspc.2 . . . . 5
75, 6anbi12d 710 . . . 4
81, 4, 7spcegf 3190 . . 3
98anabsi5 817 . 2
10 df-rex 2813 . 2
119, 10sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818  E.wrex 2808 This theorem is referenced by:  rspcev  3210  ac6c4  8882  fsumcom2  13589  infcvgaux1i  13668  fprodcom2  13788  iunmbl2  21967  esumcvg  28092  sdclem1  30236 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111
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