Theorem tpidm13 4727

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 4720	. 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴}
2		tpidm12 4726	. 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
3	1, 2	eqtr3i 2794	1 ⊢ {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}

Syntax hints:   = wceq 1567  {cpr 4596  {ctp 4598

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3or 1102  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3465  df-un 3918  df-sn 4595  df-pr 4597  df-tp 4599

This theorem is referenced by:  fntpb  7208  hashtpg  14521  hash3tpde  14529