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Theorem snsstp2 3515
 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 3513 . . 3 {𝐵} ⊆ {𝐴, 𝐵}
2 ssun1 3106 . . 3 {𝐴, 𝐵} ⊆ ({𝐴, 𝐵} ∪ {𝐶})
31, 2sstri 2954 . 2 {𝐵} ⊆ ({𝐴, 𝐵} ∪ {𝐶})
4 df-tp 3383 . 2 {𝐴, 𝐵, 𝐶} = ({𝐴, 𝐵} ∪ {𝐶})
53, 4sseqtr4i 2978 1 {𝐵} ⊆ {𝐴, 𝐵, 𝐶}
 Colors of variables: wff set class Syntax hints:   ∪ cun 2915   ⊆ wss 2917  {csn 3375  {cpr 3376  {ctp 3377 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pr 3382  df-tp 3383 This theorem is referenced by: (None)
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