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Theorem snsspr2 3639
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 3210 . 2 {𝐵} ⊆ ({𝐴} ∪ {𝐵})
2 df-pr 3504 . 2 {𝐴, 𝐵} = ({𝐴} ∪ {𝐵})
31, 2sseqtrri 3102 1 {𝐵} ⊆ {𝐴, 𝐵}
Colors of variables: wff set class
Syntax hints:  cun 3039  wss 3041  {csn 3497  {cpr 3498
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-pr 3504
This theorem is referenced by:  snsstp2  3641  ssprr  3653  ord3ex  4084  ltrelxr  7793
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