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Theorem tpidm23 3592
Description: Unordered triple  { A ,  B ,  B } is just an overlong way to write  { A ,  B }. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tpidm23  |-  { A ,  B ,  B }  =  { A ,  B }

Proof of Theorem tpidm23
StepHypRef Expression
1 tprot 3584 . 2  |-  { A ,  B ,  B }  =  { B ,  B ,  A }
2 tpidm12 3590 . 2  |-  { B ,  B ,  A }  =  { B ,  A }
3 prcom 3567 . 2  |-  { B ,  A }  =  { A ,  B }
41, 2, 33eqtri 2140 1  |-  { A ,  B ,  B }  =  { A ,  B }
Colors of variables: wff set class
Syntax hints:    = wceq 1314   {cpr 3496   {ctp 3497
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3or 946  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502  df-tp 3503
This theorem is referenced by:  tppreq3  3594
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