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Theorem sssucid 4388
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 3281 . 2  |-  A  C_  ( A  u.  { A } )
2 df-suc 4344 . 2  |-  suc  A  =  ( A  u.  { A } )
31, 2sseqtrri 3173 1  |-  A  C_  suc  A
Colors of variables: wff set class
Syntax hints:    u. cun 3110    C_ wss 3112   {csn 3571   suc csuc 4338
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-v 2724  df-un 3116  df-in 3118  df-ss 3125  df-suc 4344
This theorem is referenced by:  trsuc  4395  ordsuc  4535  0elnn  4591  sucinc  6405  sucinc2  6406  oasuc  6424  phplem4  6813  phplem4dom  6820  phplem4on  6825  fiintim  6886  fidcenumlemrk  6911  fidcenumlemr  6912  bj-nntrans  13685
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