Theorem tpidm13 4684

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 4677	. 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴}
2		tpidm12 4683	. 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵}
3	1, 2	eqtr3i 2844	1 ⊢ {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵}

Syntax hints:   = wceq 1531  {cpr 4561  {ctp 4563

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2154  ax-12 2170  ax-ext 2791

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3or 1083  df-tru 1534  df-ex 1775  df-nf 1779  df-sb 2064  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-v 3495  df-un 3939  df-sn 4560  df-pr 4562  df-tp 4564

This theorem is referenced by:  fntpb  6964  hashtpg  13835