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Theorem snsspr2 3908
Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
snsspr2  |-  { B }  C_  { A ,  B }

Proof of Theorem snsspr2
StepHypRef Expression
1 ssun2 3471 . 2  |-  { B }  C_  ( { A }  u.  { B } )
2 df-pr 3781 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3341 1  |-  { B }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 3278    C_ wss 3280   {csn 3774   {cpr 3775
This theorem is referenced by:  snsstp2  3910  ord3ex  4349  ltrelxr  9095  2strop  13522  algvsca  13558  phlip  13568  prdsvsca  13638  prdsco  13645  imasvsca  13701  ipotset  14538  lsppratlem4  16177  constr3pthlem1  21595  ex-res  21702  subfacp1lem2a  24819  dvh3dim3N  31932
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-v 2918  df-un 3285  df-in 3287  df-ss 3294  df-pr 3781
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