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Theorem snsstp2 3859
Description: A singleton is a subset of an unordered triple containing its member. (Contributed by NM, 9-Oct-2013.)
Assertion
Ref Expression
snsstp2 {B} {A, B, C}

Proof of Theorem snsstp2
StepHypRef Expression
1 snsspr2 3857 . . 3 {B} {A, B}
2 ssun1 3426 . . 3 {A, B} ({A, B} ∪ {C})
31, 2sstri 3281 . 2 {B} ({A, B} ∪ {C})
4 df-tp 3743 . 2 {A, B, C} = ({A, B} ∪ {C})
53, 4sseqtr4i 3304 1 {B} {A, B, C}
Colors of variables: wff setvar class
Syntax hints:  cun 3207   wss 3257  {csn 3737  {cpr 3738  {ctp 3739
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  df-tp 3743
This theorem is referenced by: (None)
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