New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  snsstp3 GIF version

Theorem snsstp3 3860
 Description: A singleton is a subset of an unordered triple containing its member. (Contributed by NM, 9-Oct-2013.)
Assertion
Ref Expression
snsstp3 {C} {A, B, C}

Proof of Theorem snsstp3
StepHypRef Expression
1 ssun2 3427 . 2 {C} ({A, B} ∪ {C})
2 df-tp 3743 . 2 {A, B, C} = ({A, B} ∪ {C})
31, 2sseqtr4i 3304 1 {C} {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-tp 3743 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator