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

Theorem elsucg 4950
Description: Membership in a successor. Exercise 5 of [TakeutiZaring] p. 17. (Contributed by NM, 15-Sep-1995.)
Assertion
Ref Expression
elsucg

Proof of Theorem elsucg
StepHypRef Expression
1 df-suc 4889 . . . 4
21eleq2i 2535 . . 3
3 elun 3644 . . 3
42, 3bitri 249 . 2
5 elsncg 4052 . . 3
65orbi2d 701 . 2
74, 6syl5bb 257 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818  u.cun 3473  {csn 4029  succsuc 4885
This theorem is referenced by:  elsuc  4952  elelsuc  4955  sucidg  4961  ordsssuc  4969  ordsucelsuc  6657  suc11reg  8057  nlt1pi  9305
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-sn 4030  df-suc 4889
  Copyright terms: Public domain W3C validator