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

Theorem sssucid 4660
 Description: A class is included in its own successor. Part of Proposition 7.23 of [TakeutiZaring] p. 41 (generalized to arbitrary classes). (Contributed by NM, 31-May-1994.)
Assertion
Ref Expression
sssucid

Proof of Theorem sssucid
StepHypRef Expression
1 ssun1 3512 . 2
2 df-suc 4589 . 2
31, 2sseqtr4i 3383 1
 Colors of variables: wff set class Syntax hints:   cun 3320   wss 3322  csn 3816   csuc 4585 This theorem is referenced by:  suctr  4667  trsuc  4668  suceloni  4795  limsssuc  4832  oaordi  6791  omeulem1  6827  oelim2  6840  nnaordi  6863  phplem4  7291  php  7293  onomeneq  7298  fiint  7385  cantnfval2  7626  cantnfle  7628  cantnfp1lem3  7638  cnfcomlem  7658  ranksuc  7793  fseqenlem1  7907  pwsdompw  8086  fin1a2lem12  8293  canthp1lem2  8530  nofulllem5  25663  limsucncmpi  26197  suctrALT2VD  29010  suctrALT2  29011  suctrALTcf  29096  suctrALTcfVD  29097  suctrALT3  29098 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-in 3329  df-ss 3336  df-suc 4589
 Copyright terms: Public domain W3C validator