Theorem sssucid 4337

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

Step	Hyp	Ref	Expression
1		ssun1 3239	. 2 |- A C_ ( A u. { A } )
2		df-suc 4293	. 2 |- suc A = ( A u. { A } )
3	1, 2	sseqtrri 3132	1 |- A C_ suc A

Syntax hints:   u. cun 3069   C_ wss 3071   {csn 3527   suc csuc 4287

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-suc 4293

This theorem is referenced by:  trsuc  4344  ordsuc  4478  0elnn  4532  sucinc  6341  sucinc2  6342  oasuc  6360  phplem4  6749  phplem4dom  6756  phplem4on  6761  fiintim  6817  fidcenumlemrk  6842  fidcenumlemr  6843  bj-nntrans  13149