MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tpidm13 Structured version   Visualization version   GIF version

Theorem tpidm13 4756
Description: Unordered triple {𝐴, 𝐵, 𝐴} is just an overlong way to write {𝐴, 𝐵}. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tpidm13 {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}

Proof of Theorem tpidm13
StepHypRef Expression
1 tprot 4749 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴}
2 tpidm12 4755 . 2 {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
31, 2eqtr3i 2757 1 {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534  {cpr 4626  {ctp 4628
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 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2698
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3or 1086  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-v 3471  df-un 3949  df-sn 4625  df-pr 4627  df-tp 4629
This theorem is referenced by:  fntpb  7215  hashtpg  14472
  Copyright terms: Public domain W3C validator