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Theorem snsstp3 3759
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 3314 . 2  |-  { C }  C_  ( { A ,  B }  u.  { C } )
2 df-tp 3615 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
31, 2sseqtrri 3205 1  |-  { C }  C_  { A ,  B ,  C }
Colors of variables: wff set class
Syntax hints:    u. cun 3142    C_ wss 3144   {csn 3607   {cpr 3608   {ctp 3609
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-tp 3615
This theorem is referenced by:  sstpr  3772  cnfldmul  13867
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