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Theorem snsspr1 4313
Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 27-Aug-2004.)
Assertion
Ref Expression
snsspr1 {𝐴} ⊆ {𝐴, 𝐵}

Proof of Theorem snsspr1
StepHypRef Expression
1 ssun1 3754 . 2 {𝐴} ⊆ ({𝐴} ∪ {𝐵})
2 df-pr 4151 . 2 {𝐴, 𝐵} = ({𝐴} ∪ {𝐵})
31, 2sseqtr4i 3617 1 {𝐴} ⊆ {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:  cun 3553  wss 3555  {csn 4148  {cpr 4150
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-un 3560  df-in 3562  df-ss 3569  df-pr 4151
This theorem is referenced by:  snsstp1  4315  op1stb  4901  uniop  4937  rankopb  8659  ltrelxr  10043  2strbas  15905  2strbas1  15908  phlvsca  15959  prdshom  16048  ipobas  17076  ipolerval  17077  lspprid1  18916  lsppratlem3  19068  lsppratlem4  19069  ex-dif  27134  ex-un  27135  ex-in  27136  coinflippv  30323  subfacp1lem2a  30867  altopthsn  31707  rankaltopb  31725  dvh3dim3N  36215  mapdindp2  36487  lspindp5  36536  algsca  37229  clsk1indlem2  37819  clsk1indlem3  37820  clsk1indlem1  37822  gsumpr  41424
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