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Theorem prsstp23 3670
Description: A pair is a subset of an unordered triple containing its members. (Contributed by Jim Kingdon, 11-Aug-2018.)
Assertion
Ref Expression
prsstp23  |-  { B ,  C }  C_  { A ,  B ,  C }

Proof of Theorem prsstp23
StepHypRef Expression
1 prsstp12 3668 . 2  |-  { B ,  C }  C_  { B ,  C ,  A }
2 tprot 3611 . 2  |-  { A ,  B ,  C }  =  { B ,  C ,  A }
31, 2sseqtrri 3127 1  |-  { B ,  C }  C_  { A ,  B ,  C }
Colors of variables: wff set class
Syntax hints:    C_ wss 3066   {cpr 3523   {ctp 3524
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-3or 963  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-sn 3528  df-pr 3529  df-tp 3530
This theorem is referenced by:  sstpr  3679
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