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Theorem sssucid 4198
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 3145 . 2  |-  A  C_  ( A  u.  { A } )
2 df-suc 4154 . 2  |-  suc  A  =  ( A  u.  { A } )
31, 2sseqtr4i 3041 1  |-  A  C_  suc  A
Colors of variables: wff set class
Syntax hints:    u. cun 2980    C_ wss 2982   {csn 3416   suc csuc 4148
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-suc 4154
This theorem is referenced by:  trsuc  4205  ordsuc  4334  0elnn  4386  sucinc  6110  sucinc2  6111  oasuc  6129  phplem4  6412  phplem4dom  6419  phplem4on  6424  bj-nntrans  11031
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