Theorem tpidm 4237

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 4234	. 2 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2		dfsn2 4138	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
3	1, 2	eqtr4i 2635	1 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴}

Syntax hints:   = wceq 1475  {csn 4125  {cpr 4127  {ctp 4129

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-pr 4128  df-tp 4130

This theorem is referenced by: (None)