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Theorem snsspr2 3857
 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 3427 . 2 {B} ({A} ∪ {B})
2 df-pr 3742 . 2 {A, B} = ({A} ∪ {B})
31, 2sseqtr4i 3304 1 {B} {A, B}
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3207   ⊆ wss 3257  {csn 3737  {cpr 3738 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-ss 3259  df-pr 3742 This theorem is referenced by:  snsstp2  3859
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