Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  csbidmg Unicode version

Theorem csbidmg 2985
 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 2631 . 2
2 csbnest1g 2984 . . 3
3 csbconstg 2946 . . . 4
43csbeq1d 2940 . . 3
52, 4eqtrd 2121 . 2
61, 5syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1290   wcel 1439  cvv 2620  csb 2934 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-sbc 2842  df-csb 2935 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator