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Theorem prsstp13 3712
Description: A pair is a subset of an unordered triple containing its members. (Contributed by Jim Kingdon, 11-Aug-2018.)
Assertion
Ref Expression
prsstp13  |-  { A ,  C }  C_  { A ,  B ,  C }

Proof of Theorem prsstp13
StepHypRef Expression
1 prsstp12 3711 . 2  |-  { A ,  C }  C_  { A ,  C ,  B }
2 tpcomb 3656 . 2  |-  { A ,  B ,  C }  =  { A ,  C ,  B }
31, 2sseqtrri 3163 1  |-  { A ,  C }  C_  { A ,  B ,  C }
Colors of variables: wff set class
Syntax hints:    C_ wss 3102   {cpr 3562   {ctp 3563
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-3or 964  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-sn 3567  df-pr 3568  df-tp 3569
This theorem is referenced by:  sstpr  3722
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