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Theorem snsstp3 3768
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 3339 . 2  |-  { C }  C_  ( { A ,  B }  u.  { C } )
2 df-tp 3648 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
31, 2sseqtr4i 3211 1  |-  { C }  C_  { A ,  B ,  C }
Colors of variables: wff set class
Syntax hints:    u. cun 3150    C_ wss 3152   {csn 3640   {cpr 3641   {ctp 3642
This theorem is referenced by:  fr3nr  4571  rngmulr  13258  srngmulr  13266  lmodsca  13275  algmulr  13280  phlsca  13290  topgrptset  13298  otpsle  13305  odrngmulr  13314  odrngds  13317  prdsmulr  13359  prdsds  13363  imasds  13416  imasmulr  13421  fuccofval  13833  setccofval  13914  catccofval  13932  xpccofval  13956  psrmulr  16129  cnfldmul  16385  cnfldds  16389
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-in 3159  df-ss 3166  df-tp 3648
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