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Theorem sssucid 4433
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 3313 . 2  |-  A  C_  ( A  u.  { A } )
2 df-suc 4389 . 2  |-  suc  A  =  ( A  u.  { A } )
31, 2sseqtrri 3205 1  |-  A  C_  suc  A
Colors of variables: wff set class
Syntax hints:    u. cun 3142    C_ wss 3144   {csn 3607   suc csuc 4383
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-suc 4389
This theorem is referenced by:  trsuc  4440  ordsuc  4580  0elnn  4636  sucinc  6471  sucinc2  6472  oasuc  6490  phplem4  6884  phplem4dom  6891  phplem4on  6896  fiintim  6958  fidcenumlemrk  6984  fidcenumlemr  6985  bj-nntrans  15181
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