Theorem tpidm23 4292

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 4284	. 2 ⊢ {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2		tpidm12 4290	. 2 ⊢ {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3		prcom 4267	. 2 ⊢ {𝐵, 𝐴} = {𝐴, 𝐵}
4	1, 2, 3	3eqtri 2648	1 ⊢ {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}

Syntax hints:   = wceq 1483  {cpr 4179  {ctp 4181

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1038  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-sn 4178  df-pr 4180  df-tp 4182

This theorem is referenced by:  tppreq3  4294  fntpb  6473  hashtpg  13267