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Theorem snsspr2 3891
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 3454 . 2  |-  { B }  C_  ( { A }  u.  { B } )
2 df-pr 3764 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3324 1  |-  { B }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 3261    C_ wss 3263   {csn 3757   {cpr 3758
This theorem is referenced by:  snsstp2  3893  ord3ex  4330  ltrelxr  9072  2strop  13494  algvsca  13530  phlip  13540  prdsvsca  13610  prdsco  13617  imasvsca  13673  ipotset  14510  lsppratlem4  16149  constr3pthlem1  21490  ex-res  21597  subfacp1lem2a  24645  dvh3dim3N  31564
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 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
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 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-v 2901  df-un 3268  df-in 3270  df-ss 3277  df-pr 3764
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