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Theorem snsstp3 4381
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 3810 . 2 {𝐶} ⊆ ({𝐴, 𝐵} ∪ {𝐶})
2 df-tp 4215 . 2 {𝐴, 𝐵, 𝐶} = ({𝐴, 𝐵} ∪ {𝐶})
31, 2sseqtr4i 3671 1 {𝐶} ⊆ {𝐴, 𝐵, 𝐶}
Colors of variables: wff setvar class
Syntax hints:  cun 3605  wss 3607  {csn 4210  {cpr 4212  {ctp 4214
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-un 3612  df-in 3614  df-ss 3621  df-tp 4215
This theorem is referenced by:  fr3nr  7021  rngmulr  16050  srngmulr  16058  lmodsca  16067  ipsmulr  16074  ipsip  16077  phlsca  16084  topgrptset  16092  otpsle  16101  otpsleOLD  16105  odrngmulr  16116  odrngds  16119  prdsmulr  16166  prdsip  16168  prdsds  16171  imasds  16220  imasmulr  16225  imasip  16228  fuccofval  16666  setccofval  16779  catccofval  16797  estrccofval  16816  xpccofval  16869  psrmulr  19432  cnfldmul  19800  cnfldds  19804  trkgitv  25391  signswch  30766  algmulr  38067  clsk1indlem1  38660  rngccofvalALTV  42312  ringccofvalALTV  42375
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