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Theorem snsspr1 4533
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 3974 . 2 {𝐴} ⊆ ({𝐴} ∪ {𝐵})
2 df-pr 4371 . 2 {𝐴, 𝐵} = ({𝐴} ∪ {𝐵})
31, 2sseqtr4i 3834 1 {𝐴} ⊆ {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:  cun 3767  wss 3769  {csn 4368  {cpr 4370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-ext 2777
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-v 3387  df-un 3774  df-in 3776  df-ss 3783  df-pr 4371
This theorem is referenced by:  snsstp1  4535  op1stb  5130  uniop  5171  rankopb  8965  ltrelxr  10389  2strbas  16305  2strbas1  16308  phlvsca  16359  prdshom  16442  ipobas  17470  ipolerval  17471  lspprid1  19318  lsppratlem3  19472  lsppratlem4  19473  ex-dif  27808  ex-un  27809  ex-in  27810  coinflippv  31062  subfacp1lem2a  31679  altopthsn  32581  rankaltopb  32599  dvh3dim3N  37470  mapdindp2  37742  lspindp5  37791  algsca  38536  clsk1indlem2  39122  clsk1indlem3  39123  clsk1indlem1  39125  gsumpr  42938
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