Theorem tpidm23 4722

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 4714	. 2 ⊢ {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2		tpidm12 4720	. 2 ⊢ {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3		prcom 4697	. 2 ⊢ {𝐵, 𝐴} = {𝐴, 𝐵}
4	1, 2, 3	3eqtri 2789	1 ⊢ {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}

This proof depends on syntax axioms:   = wceq 1569  {cpr 4590  {ctp 4592

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3or 1103  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-un 3909  df-sn 4589  df-pr 4591  df-tp 4593

This theorem is used by:  tppreq3  4724  fntpb  7207  hashtpg  14529  hash3tpde  14537