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Theorem snsspr1 4120
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 3617 . 2  |-  { A }  C_  ( { A }  u.  { B } )
2 df-pr 3978 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3487 1  |-  { A }  C_  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    u. cun 3424    C_ wss 3426   {csn 3975   {cpr 3977
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 3070  df-un 3431  df-in 3433  df-ss 3440  df-pr 3978
This theorem is referenced by:  snsstp1  4122  op1stb  4660  uniop  4692  rankopb  8160  ltrelxr  9539  2strbas  14377  phlvsca  14425  prdshom  14507  ipobas  15427  ipolerval  15428  lspprid1  17184  lsppratlem3  17336  lsppratlem4  17337  constr3pthlem1  23676  ex-dif  23765  ex-un  23766  ex-in  23767  coinflippv  27000  signswbase  27089  subfacp1lem2a  27202  altopthsn  28126  rankaltopb  28144  algsca  29676  gsumpr  30896  dvh3dim3N  35400  mapdindp2  35672  lspindp5  35721
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