Theorem tpidm

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

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

Proof

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