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Theorem snsspr1 4164
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 3652 . 2  |-  { A }  C_  ( { A }  u.  { B } )
2 df-pr 4017 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3522 1  |-  { A }  C_  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    u. cun 3459    C_ wss 3461   {csn 4014   {cpr 4016
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-v 3097  df-un 3466  df-in 3468  df-ss 3475  df-pr 4017
This theorem is referenced by:  snsstp1  4166  op1stb  4707  uniop  4740  rankopb  8273  ltrelxr  9651  2strbas  14611  phlvsca  14659  prdshom  14741  ipobas  15659  ipolerval  15660  lspprid1  17517  lsppratlem3  17669  lsppratlem4  17670  constr3pthlem1  24527  ex-dif  25016  ex-un  25017  ex-in  25018  coinflippv  28295  subfacp1lem2a  28497  altopthsn  29586  rankaltopb  29604  algsca  31106  gsumpr  32683  dvh3dim3N  36916  mapdindp2  37188  lspindp5  37237
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