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Theorem rspce 2950
 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:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rspce
StepHypRef Expression
1 nfcv 2489 . . . 4
2 nfv 1619 . . . . 5
3 rspc.1 . . . . 5
42, 3nfan 1824 . . . 4
5 eleq1 2413 . . . . 5
6 rspc.2 . . . . 5
75, 6anbi12d 691 . . . 4
81, 4, 7spcegf 2935 . . 3
98anabsi5 790 . 2
10 df-rex 2620 . 2
119, 10sylibr 203 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541  wnf 1544   wceq 1642   wcel 1710  wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-v 2861 This theorem is referenced by:  rspcev  2955
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