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Theorem sssucid 4362
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 3248 . 2  |-  A  C_  ( A  u.  { A } )
2 df-suc 4291 . 2  |-  suc  A  =  ( A  u.  { A } )
31, 2sseqtr4i 3132 1  |-  A  C_  suc  A
Colors of variables: wff set class
Syntax hints:    u. cun 3076    C_ wss 3078   {csn 3544   suc csuc 4287
This theorem is referenced by:  trsuc  4369  suceloni  4495  limsssuc  4532  oaordi  6430  omeulem1  6466  oelim2  6479  nnaordi  6502  phplem4  6928  php  6930  onomeneq  6935  fiint  7018  cantnfval2  7254  cantnfle  7256  cantnfp1lem3  7266  cnfcomlem  7286  ranksuc  7421  fseqenlem1  7535  pwsdompw  7714  fin1a2lem12  7921  canthp1lem2  8155  axfelem13  23526  axfelem18  23531  limsucncmpi  24058  suctrALT2VD  27399  suctrALT2  27400  suctrALTcf  27485  suctrALTcfVD  27486  suctrALT3  27487  suctrALT4  27491
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083  df-in 3085  df-ss 3089  df-suc 4291
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