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Theorem rspc 2650
 Description: Restricted specialization, using implicit substitution. (Contributed by NM, 19-Apr-2005.) (Revised by Mario Carneiro, 11-Oct-2016.)
Hypotheses
Ref Expression
rspc.1
rspc.2
Assertion
Ref Expression
rspc
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rspc
StepHypRef Expression
1 df-ral 2311 . 2
2 nfcv 2178 . . . 4
3 nfv 1421 . . . . 5
4 rspc.1 . . . . 5
53, 4nfim 1464 . . . 4
6 eleq1 2100 . . . . 5
7 rspc.2 . . . . 5
86, 7imbi12d 223 . . . 4
92, 5, 8spcgf 2635 . . 3
109pm2.43a 45 . 2
111, 10syl5bi 141 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243  wnf 1349   wcel 1393  wral 2306 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559 This theorem is referenced by:  rspcv  2652  rspc2  2661  pofun  4049  fmptcof  5331  fliftfuns  5438  qliftfuns  6190  bj-nntrans  10076
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