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Theorem snsspr2 3781
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 3352 . 2  |-  { B }  C_  ( { A }  u.  { B } )
2 df-pr 3660 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3224 1  |-  { B }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 3163    C_ wss 3165   {csn 3653   {cpr 3654
This theorem is referenced by:  snsstp2  3783  ord3ex  4216  ltrelxr  8902  2strop  13262  algvsca  13298  phlip  13308  prdsvsca  13376  prdsco  13383  imasvsca  13439  ipotset  14276  lsppratlem4  15919  ex-res  20844  subfacp1lem2a  23726  constr3pthlem1  28401  dvh3dim3N  32261
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-pr 3660
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