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Theorem snsspr2 3844
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 3415 . 2  |-  { B }  C_  ( { A }  u.  { B } )
2 df-pr 3723 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3287 1  |-  { B }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 3226    C_ wss 3228   {csn 3716   {cpr 3717
This theorem is referenced by:  snsstp2  3846  ord3ex  4279  ltrelxr  8973  2strop  13337  algvsca  13373  phlip  13383  prdsvsca  13453  prdsco  13460  imasvsca  13516  ipotset  14353  lsppratlem4  15996  ex-res  20934  subfacp1lem2a  24115  constr3pthlem1  27762  dvh3dim3N  31691
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-v 2866  df-un 3233  df-in 3235  df-ss 3242  df-pr 3723
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