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

Step	Hyp	Ref	Expression
1		ssun2 3314	. 2 |- { C } C_ ( { A , B } u. { C } )
2		df-tp 3615	. 2 |- { A , B , C } = ( { A , B } u. { C } )
3	1, 2	sseqtrri 3205	1 |- { C } C_ { A , B , C }

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