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

Theorem csbidmg 3306
 Description: Idempotent law for class substitutions. (Contributed by NM, 1-Mar-2008.)
Assertion
Ref Expression
csbidmg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem csbidmg
StepHypRef Expression
1 elex 2966 . 2
2 csbnest1g 3305 . . 3
3 csbconstg 3267 . . . 4
43csbeq1d 3259 . . 3
52, 4eqtrd 2470 . 2
61, 5syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726  cvv 2958  csb 3253 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-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164  df-csb 3254
 Copyright terms: Public domain W3C validator