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Theorem rspc3v 2665
 Description: 3-variable restricted specialization, using implicit substitution. (Contributed by NM, 10-May-2005.)
Hypotheses
Ref Expression
rspc3v.1
rspc3v.2
rspc3v.3
Assertion
Ref Expression
rspc3v
Distinct variable groups:   ,   ,   ,   ,,,   ,,   ,   ,   ,,   ,,,
Allowed substitution hints:   (,,)   (,)   (,)   (,)   ()   (,)   (,)   ()

Proof of Theorem rspc3v
StepHypRef Expression
1 rspc3v.1 . . . . 5
21ralbidv 2326 . . . 4
3 rspc3v.2 . . . . 5
43ralbidv 2326 . . . 4
52, 4rspc2v 2662 . . 3
6 rspc3v.3 . . . 4
76rspcv 2652 . . 3
85, 7sylan9 389 . 2
983impa 1099 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   w3a 885   wceq 1243   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-3an 887  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:  swopolem  4042  isopolem  5461  isosolem  5463  caovassg  5659  caovcang  5662  caovordig  5666  caovordg  5668  caovdig  5675  caovdirg  5678  caoftrn  5736
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