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Theorem snsspr2 4773
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 4131 . 2 {𝐵} ⊆ ({𝐴} ∪ {𝐵})
2 df-pr 4587 . 2 {𝐴, 𝐵} = ({𝐴} ∪ {𝐵})
31, 2sseqtrri 3979 1 {𝐵} ⊆ {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:  cun 3906  wss 3908  {csn 4584  {cpr 4586
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3445  df-un 3913  df-in 3915  df-ss 3925  df-pr 4587
This theorem is referenced by:  snsstp2  4775  ord3ex  5340  ltrelxr  11212  2strop  17099  2strop1  17103  phlip  17224  prdsco  17342  ipotset  18414  gsumpr  19723  lsppratlem4  20596  ex-res  29271  subfacp1lem2a  33643  dvh3dim3N  39879  algvsca  41447  corclrcl  41921  mnuprdlem4  42497
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