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Theorem sssucid 5719
 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 ⊆ suc 𝐴

Proof of Theorem sssucid
StepHypRef Expression
1 ssun1 3738 . 2 𝐴 ⊆ (𝐴 ∪ {𝐴})
2 df-suc 5646 . 2 suc 𝐴 = (𝐴 ∪ {𝐴})
31, 2sseqtr4i 3601 1 𝐴 ⊆ suc 𝐴
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3538   ⊆ wss 3540  {csn 4125  suc csuc 5642 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-in 3547  df-ss 3554  df-suc 5646 This theorem is referenced by:  trsuc  5727  suceloni  6905  limsssuc  6942  oaordi  7513  omeulem1  7549  oelim2  7562  nnaordi  7585  phplem4  8027  php  8029  onomeneq  8035  fiint  8122  cantnfval2  8449  cantnfle  8451  cantnfp1lem3  8460  cnfcomlem  8479  ranksuc  8611  fseqenlem1  8730  pwsdompw  8909  fin1a2lem12  9116  canthp1lem2  9354  nofulllem5  31105  limsucncmpi  31614  finxpreclem3  32406  clsk1independent  37364  suctrALT  38083  suctrALT2VD  38093  suctrALT2  38094  suctrALTcf  38180  suctrALTcfVD  38181  suctrALT3  38182
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