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Theorem tpidm23 4283
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 4275 . 2 {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2 tpidm12 4281 . 2 {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3 prcom 4258 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
41, 2, 33eqtri 2646 1 {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1481  {cpr 4170  {ctp 4172
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1037  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-v 3197  df-un 3572  df-sn 4169  df-pr 4171  df-tp 4173
This theorem is referenced by:  tppreq3  4285  fntpb  6458  hashtpg  13250
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