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Theorem snsspr2 4708
 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 4100 . 2 {𝐵} ⊆ ({𝐴} ∪ {𝐵})
2 df-pr 4528 . 2 {𝐴, 𝐵} = ({𝐴} ∪ {𝐵})
31, 2sseqtrri 3952 1 {𝐵} ⊆ {𝐴, 𝐵}
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3879   ⊆ wss 3881  {csn 4525  {cpr 4527 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-pr 4528 This theorem is referenced by:  snsstp2  4710  ord3ex  5254  ltrelxr  10694  2strop  16599  2strop1  16602  phlip  16653  prdsco  16736  ipotset  17762  gsumpr  19072  lsppratlem4  19919  ex-res  28236  subfacp1lem2a  32555  dvh3dim3N  38764  algvsca  40169  corclrcl  40451  mnuprdlem4  41026
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