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Theorem snsspr2 4314
 Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
snsspr2 {𝐵} ⊆ {𝐴, 𝐵}

Proof of Theorem snsspr2
StepHypRef Expression
1 ssun2 3755 . 2 {𝐵} ⊆ ({𝐴} ∪ {𝐵})
2 df-pr 4151 . 2 {𝐴, 𝐵} = ({𝐴} ∪ {𝐵})
31, 2sseqtr4i 3617 1 {𝐵} ⊆ {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:  snsstp2  4316  ord3ex  4816  ltrelxr  10043  2strop  15906  2strop1  15909  phlip  15960  prdsco  16049  ipotset  17078  lsppratlem4  19069  ex-res  27152  subfacp1lem2a  30867  dvh3dim3N  36215  algvsca  37230  corclrcl  37477  gsumpr  41424
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