Theorem tpidm13 4755

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

Step	Hyp	Ref	Expression
1		tprot 4748	. 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴}
2		tpidm12 4754	. 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
3	1, 2	eqtr3i 2756	1 ⊢ {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}

Syntax hints:   = wceq 1533  {cpr 4625  {ctp 4627

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 2697

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 2704  df-cleq 2718  df-clel 2804  df-v 3470  df-un 3948  df-sn 4624  df-pr 4626  df-tp 4628

This theorem is referenced by:  fntpb  7205  hashtpg  14449