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Theorem snsstp3 3544
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 3135 . 2 {𝐶} ⊆ ({𝐴, 𝐵} ∪ {𝐶})
2 df-tp 3411 . 2 {𝐴, 𝐵, 𝐶} = ({𝐴, 𝐵} ∪ {𝐶})
31, 2sseqtr4i 3006 1 {𝐶} ⊆ {𝐴, 𝐵, 𝐶}
Colors of variables: wff set class
Syntax hints:  cun 2943  wss 2945  {csn 3403  {cpr 3404  {ctp 3405
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-tp 3411
This theorem is referenced by:  sstpr  3556
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