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Theorem snsspr1 3801
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 3372 . 2  |-  { A }  C_  ( { A }  u.  { B } )
2 df-pr 3681 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3245 1  |-  { A }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 3184    C_ wss 3186   {csn 3674   {cpr 3675
This theorem is referenced by:  snsstp1  3803  uniop  4306  op1stb  4606  rankopb  7569  ltrelxr  8931  2strbas  13292  algsca  13328  phlvsca  13338  prdssca  13405  prdshom  13415  imassca  13471  ipobas  14307  ipolerval  14308  lspprid1  15803  lsppratlem3  15951  lsppratlem4  15952  ex-dif  20863  ex-un  20864  ex-in  20865  coinflippv  23915  subfacp1lem2a  23995  altopthsn  24881  rankaltopb  24899  constr3pthlem1  27539  dvh3dim3N  31457  mapdindp2  31729  lspindp5  31778
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-v 2824  df-un 3191  df-in 3193  df-ss 3200  df-pr 3681
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