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Theorem snsstp3 3943
Description: A singleton is a subset of an unordered triple containing its member. (Contributed by NM, 9-Oct-2013.)
Assertion
Ref Expression
snsstp3  |-  { C }  C_  { A ,  B ,  C }

Proof of Theorem snsstp3
StepHypRef Expression
1 ssun2 3503 . 2  |-  { C }  C_  ( { A ,  B }  u.  { C } )
2 df-tp 3814 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
31, 2sseqtr4i 3373 1  |-  { C }  C_  { A ,  B ,  C }
Colors of variables: wff set class
Syntax hints:    u. cun 3310    C_ wss 3312   {csn 3806   {cpr 3807   {ctp 3808
This theorem is referenced by:  fr3nr  4752  rngmulr  13571  srngmulr  13579  lmodsca  13588  algmulr  13593  phlsca  13603  topgrptset  13611  otpsle  13618  odrngmulr  13629  odrngds  13632  prdsmulr  13674  prdsds  13678  imasds  13731  imasmulr  13736  fuccofval  14148  setccofval  14229  catccofval  14247  xpccofval  14271  psrmulr  16440  cnfldmul  16701  cnfldds  16705
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-in 3319  df-ss 3326  df-tp 3814
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