Theorem tpidm 4740

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 4737	. 2 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2		dfsn2 4621	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
3	1, 2	eqtr4i 2760	1 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴}

Syntax hints:   = wceq 1539  {csn 4608  {cpr 4610  {ctp 4612

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-v 3466  df-un 3938  df-pr 4611  df-tp 4613

This theorem is referenced by: (None)