Theorem tpidm 4717

Description: Unordered triple {𝐴, 𝐴, 𝐴} is just an overlong way to write {𝐴}. (Contributed by David A. Wheeler, 10-May-2015.)

Assertion

Ref	Expression
tpidm	⊢ {𝐴, 𝐴, 𝐴} = {𝐴}

Proof of Theorem tpidm

Step	Hyp	Ref	Expression
1		tpidm12 4714	. 2 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2		dfsn2 4595	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
3	1, 2	eqtr4i 2763	1 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴}

Syntax hints:   = wceq 1542  {csn 4582  {cpr 4584  {ctp 4586

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3444  df-un 3908  df-pr 4585  df-tp 4587

This theorem is referenced by: (None)