Theorem tpidm23 4753

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

Step	Hyp	Ref	Expression
1		tprot 4745	. 2 ⊢ {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2		tpidm12 4751	. 2 ⊢ {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3		prcom 4728	. 2 ⊢ {𝐵, 𝐴} = {𝐴, 𝐵}
4	1, 2, 3	3eqtri 2756	1 ⊢ {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}

Syntax hints:   = wceq 1533  {cpr 4622  {ctp 4624

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3or 1085  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-un 3945  df-sn 4621  df-pr 4623  df-tp 4625

This theorem is referenced by:  tppreq3  4755  fntpb  7202  hashtpg  14442