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Theorem snsspr1 4176
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 3667 . 2  |-  { A }  C_  ( { A }  u.  { B } )
2 df-pr 4030 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3537 1  |-  { A }  C_  { A ,  B }
Colors of variables: wff setvar class
Syntax hints:    u. cun 3474    C_ wss 3476   {csn 4027   {cpr 4029
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-un 3481  df-in 3483  df-ss 3490  df-pr 4030
This theorem is referenced by:  snsstp1  4178  op1stb  4717  uniop  4750  rankopb  8266  ltrelxr  9644  2strbas  14588  phlvsca  14636  prdshom  14718  ipobas  15638  ipolerval  15639  lspprid1  17426  lsppratlem3  17578  lsppratlem4  17579  constr3pthlem1  24331  ex-dif  24821  ex-un  24822  ex-in  24823  coinflippv  28062  signswbase  28151  subfacp1lem2a  28264  altopthsn  29188  rankaltopb  29206  algsca  30735  gsumpr  32014  dvh3dim3N  36246  mapdindp2  36518  lspindp5  36567
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