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Theorem snsstp2 3707
 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 3705 . . 3 {𝐵} ⊆ {𝐴, 𝐵}
2 ssun1 3270 . . 3 {𝐴, 𝐵} ⊆ ({𝐴, 𝐵} ∪ {𝐶})
31, 2sstri 3137 . 2 {𝐵} ⊆ ({𝐴, 𝐵} ∪ {𝐶})
4 df-tp 3568 . 2 {𝐴, 𝐵, 𝐶} = ({𝐴, 𝐵} ∪ {𝐶})
53, 4sseqtrri 3163 1 {𝐵} ⊆ {𝐴, 𝐵, 𝐶}
 Colors of variables: wff set class Syntax hints:   ∪ cun 3100   ⊆ wss 3102  {csn 3560  {cpr 3561  {ctp 3562 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-pr 3567  df-tp 3568 This theorem is referenced by: (None)
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