Theorem tpidm23 4782

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 4774	. 2 ⊢ {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2		tpidm12 4780	. 2 ⊢ {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3		prcom 4757	. 2 ⊢ {𝐵, 𝐴} = {𝐴, 𝐵}
4	1, 2, 3	3eqtri 2772	1 ⊢ {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}

Syntax hints:   = wceq 1537  {cpr 4650  {ctp 4652

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3or 1088  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-un 3981  df-sn 4649  df-pr 4651  df-tp 4653

This theorem is referenced by:  tppreq3  4784  fntpb  7246  hashtpg  14534  hash3tpde  14542