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Theorem tpidm23 4685
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 4677 . 2 {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2 tpidm12 4683 . 2 {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3 prcom 4660 . 2 {𝐵, 𝐴} = {𝐴, 𝐵}
41, 2, 33eqtri 2846 1 {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1531  {cpr 4561  {ctp 4563
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2154  ax-12 2170  ax-ext 2791
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3or 1083  df-tru 1534  df-ex 1775  df-nf 1779  df-sb 2064  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-v 3495  df-un 3939  df-sn 4560  df-pr 4562  df-tp 4564
This theorem is referenced by:  tppreq3  4687  fntpb  6964  hashtpg  13835
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