New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  rspc3v Unicode version

Theorem rspc3v 2964
 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 2634 . . . 4
3 rspc3v.2 . . . . 5
43ralbidv 2634 . . . 4
52, 4rspc2v 2961 . . 3
6 rspc3v.3 . . . 4
76rspcv 2951 . . 3
85, 7sylan9 638 . 2
983impa 1146 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934   wceq 1642   wcel 1710  wral 2614 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-3an 936  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-ral 2619  df-v 2861 This theorem is referenced by:  caovassg  5626  caovdig  5632  caovdirg  5633  trd  5921
 Copyright terms: Public domain W3C validator