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Theorem snsspr1 3780
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 3351 . 2  |-  { A }  C_  ( { A }  u.  { B } )
2 df-pr 3660 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3224 1  |-  { A }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 3163    C_ wss 3165   {csn 3653   {cpr 3654
This theorem is referenced by:  snsstp1  3782  uniop  4285  op1stb  4585  rankopb  7540  ltrelxr  8902  2strbas  13261  algsca  13297  phlvsca  13307  prdssca  13372  prdshom  13382  imassca  13438  ipobas  14274  ipolerval  14275  lspprid1  15770  lsppratlem3  15918  lsppratlem4  15919  ex-dif  20826  ex-un  20827  ex-in  20828  coinflippv  23699  subfacp1lem2a  23726  altopthsn  24567  rankaltopb  24585  constr3pthlem1  28401  dvh3dim3N  32261  mapdindp2  32533  lspindp5  32582
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-in 3172  df-ss 3179  df-pr 3660
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