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Theorem tpidm23 3708
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 3700 . 2 {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2 tpidm12 3706 . 2 {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3 prcom 3683 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
41, 2, 33eqtri 2214 1 {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}
Colors of variables: wff set class
Syntax hints:   = wceq 1364  {cpr 3608  {ctp 3609
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-3or 981  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614  df-tp 3615
This theorem is referenced by:  tppreq3  3710
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