Theorem tpidm13 4713

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 4706	. 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴}
2		tpidm12 4712	. 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
3	1, 2	eqtr3i 2761	1 ⊢ {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}

Syntax hints:   = wceq 1541  {cpr 4582  {ctp 4584

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-un 3906  df-sn 4581  df-pr 4583  df-tp 4585

This theorem is referenced by:  fntpb  7155  hashtpg  14408  hash3tpde  14416