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Theorem snsspr2 4124
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 3621 . 2  |-  { B }  C_  ( { A }  u.  { B } )
2 df-pr 3981 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3490 1  |-  { B }  C_  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    u. cun 3427    C_ wss 3429   {csn 3978   {cpr 3980
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-v 3073  df-un 3434  df-in 3436  df-ss 3443  df-pr 3981
This theorem is referenced by:  snsstp2  4126  ord3ex  4583  ltrelxr  9542  2strop  14387  phlip  14435  prdsco  14517  ipotset  15438  lsppratlem4  17346  constr3pthlem1  23686  ex-res  23793  signswplusg  27093  subfacp1lem2a  27205  algvsca  29680  gsumpr  30899  dvh3dim3N  35403
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