Theorem tpidm 4722

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 4719	. 2 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2		dfsn2 4602	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
3	1, 2	eqtr4i 2755	1 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴}

Syntax hints:   = wceq 1540  {csn 4589  {cpr 4591  {ctp 4593

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-un 3919  df-pr 4592  df-tp 4594

This theorem is referenced by: (None)