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Theorem sssucid 4485
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  |-  A  C_  suc  A

Proof of Theorem sssucid
StepHypRef Expression
1 ssun1 3351 . 2  |-  A  C_  ( A  u.  { A } )
2 df-suc 4414 . 2  |-  suc  A  =  ( A  u.  { A } )
31, 2sseqtr4i 3224 1  |-  A  C_  suc  A
Colors of variables: wff set class
Syntax hints:    u. cun 3163    C_ wss 3165   {csn 3653   suc csuc 4410
This theorem is referenced by:  trsuc  4492  suceloni  4620  limsssuc  4657  oaordi  6560  omeulem1  6596  oelim2  6609  nnaordi  6632  phplem4  7059  php  7061  onomeneq  7066  fiint  7149  cantnfval2  7386  cantnfle  7388  cantnfp1lem3  7398  cnfcomlem  7418  ranksuc  7553  fseqenlem1  7667  pwsdompw  7846  fin1a2lem12  8053  canthp1lem2  8291  nofulllem5  24431  limsucncmpi  24956  suctrALT2VD  28928  suctrALT2  28929  suctrALTcf  29014  suctrALTcfVD  29015  suctrALT3  29016  suctrALT4  29020
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-in 3172  df-ss 3179  df-suc 4414
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