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Theorem prsstp12 3598
Description: A pair is a subset of an unordered triple containing its members. (Contributed by Jim Kingdon, 11-Aug-2018.)
Assertion
Ref Expression
prsstp12 {𝐴, 𝐵} ⊆ {𝐴, 𝐵, 𝐶}

Proof of Theorem prsstp12
StepHypRef Expression
1 ssun1 3166 . 2 {𝐴, 𝐵} ⊆ ({𝐴, 𝐵} ∪ {𝐶})
2 df-tp 3460 . 2 {𝐴, 𝐵, 𝐶} = ({𝐴, 𝐵} ∪ {𝐶})
31, 2sseqtr4i 3062 1 {𝐴, 𝐵} ⊆ {𝐴, 𝐵, 𝐶}
Colors of variables: wff set class
Syntax hints:  cun 3000  wss 3002  {csn 3452  {cpr 3453  {ctp 3454
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2624  df-un 3006  df-in 3008  df-ss 3015  df-tp 3460
This theorem is referenced by:  prsstp13  3599  prsstp23  3600  sstpr  3609
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