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Theorem snsspr2 3948
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 3511 . 2  |-  { B }  C_  ( { A }  u.  { B } )
2 df-pr 3821 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3381 1  |-  { B }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 3318    C_ wss 3320   {csn 3814   {cpr 3815
This theorem is referenced by:  snsstp2  3950  ord3ex  4389  ltrelxr  9139  2strop  13567  algvsca  13603  phlip  13613  prdsvsca  13683  prdsco  13690  imasvsca  13746  ipotset  14583  lsppratlem4  16222  constr3pthlem1  21642  ex-res  21749  subfacp1lem2a  24866  dvh3dim3N  32247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-un 3325  df-in 3327  df-ss 3334  df-pr 3821
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