ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sssucid Unicode version

Theorem sssucid 4253
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 3166 . 2  |-  A  C_  ( A  u.  { A } )
2 df-suc 4209 . 2  |-  suc  A  =  ( A  u.  { A } )
31, 2sseqtr4i 3062 1  |-  A  C_  suc  A
Colors of variables: wff set class
Syntax hints:    u. cun 3000    C_ wss 3002   {csn 3452   suc csuc 4203
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2624  df-un 3006  df-in 3008  df-ss 3015  df-suc 4209
This theorem is referenced by:  trsuc  4260  ordsuc  4394  0elnn  4447  sucinc  6222  sucinc2  6223  oasuc  6241  phplem4  6627  phplem4dom  6634  phplem4on  6639  fiintim  6695  fidcenumlemrk  6719  fidcenumlemr  6720  bj-nntrans  12150
  Copyright terms: Public domain W3C validator