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Theorem snsspr1 4093
Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 27-Aug-2004.)
Assertion
Ref Expression
snsspr1  |-  { A }  C_  { A ,  B }

Proof of Theorem snsspr1
StepHypRef Expression
1 ssun1 3581 . 2  |-  { A }  C_  ( { A }  u.  { B } )
2 df-pr 3947 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3450 1  |-  { A }  C_  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    u. cun 3387    C_ wss 3389   {csn 3944   {cpr 3946
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-10 1845  ax-11 1850  ax-12 1862  ax-13 2006  ax-ext 2360
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1402  df-ex 1621  df-nf 1625  df-sb 1748  df-clab 2368  df-cleq 2374  df-clel 2377  df-nfc 2532  df-v 3036  df-un 3394  df-in 3396  df-ss 3403  df-pr 3947
This theorem is referenced by:  snsstp1  4095  op1stb  4632  uniop  4664  rankopb  8183  ltrelxr  9559  2strbas  14743  phlvsca  14791  prdshom  14874  ipobas  15902  ipolerval  15903  lspprid1  17756  lsppratlem3  17908  lsppratlem4  17909  constr3pthlem1  24776  ex-dif  25265  ex-un  25266  ex-in  25267  coinflippv  28605  subfacp1lem2a  28813  altopthsn  29764  rankaltopb  29782  algsca  31298  gsumpr  33150  dvh3dim3N  37589  mapdindp2  37861  lspindp5  37910
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