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Theorem snsstp3 3784
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 3352 . 2  |-  { C }  C_  ( { A ,  B }  u.  { C } )
2 df-tp 3661 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
31, 2sseqtr4i 3224 1  |-  { C }  C_  { A ,  B ,  C }
Colors of variables: wff set class
Syntax hints:    u. cun 3163    C_ wss 3165   {csn 3653   {cpr 3654   {ctp 3655
This theorem is referenced by:  fr3nr  4587  rngmulr  13274  srngmulr  13282  lmodsca  13291  algmulr  13296  phlsca  13306  topgrptset  13314  otpsle  13321  odrngmulr  13330  odrngds  13333  prdsmulr  13375  prdsds  13379  imasds  13432  imasmulr  13437  fuccofval  13849  setccofval  13930  catccofval  13948  xpccofval  13972  psrmulr  16145  cnfldmul  16401  cnfldds  16405
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-in 3172  df-ss 3179  df-tp 3661
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