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Theorem prsstp23 3542
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 3540 . 2  |-  { B ,  C }  C_  { B ,  C ,  A }
2 tprot 3487 . 2  |-  { A ,  B ,  C }  =  { B ,  C ,  A }
31, 2sseqtr4i 3033 1  |-  { B ,  C }  C_  { A ,  B ,  C }
Colors of variables: wff set class
Syntax hints:    C_ wss 2974   {cpr 3401   {ctp 3402
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-3or 921  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-sn 3406  df-pr 3407  df-tp 3408
This theorem is referenced by:  sstpr  3551
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