Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbcreug Structured version   Unicode version

Theorem sbcreug 3239
 Description: Interchange class substitution and restricted uniqueness quantifier. (Contributed by NM, 24-Feb-2013.)
Assertion
Ref Expression
sbcreug
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()   (,)

Proof of Theorem sbcreug
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3166 . 2
2 dfsbcq2 3166 . . 3
32reubidv 2894 . 2
4 nfcv 2574 . . . 4
5 nfs1v 2184 . . . 4
64, 5nfreu 2884 . . 3
7 sbequ12 1945 . . . 4
87reubidv 2894 . . 3
96, 8sbie 2152 . 2
101, 3, 9vtoclbg 3014 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653  wsb 1659   wcel 1726  wreu 2709  wsbc 3163 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-reu 2714  df-v 2960  df-sbc 3164
 Copyright terms: Public domain W3C validator