Theorem tpidm23

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

	Ref	Expression
Assertion	tpidm23	⊢ { 𝐴 , 𝐵 , 𝐵 } = { 𝐴 , 𝐵 }

Proof

Step	Hyp	Ref	Expression
1		tprot	⊢ { 𝐴 , 𝐵 , 𝐵 } = { 𝐵 , 𝐵 , 𝐴 }
2		tpidm12	⊢ { 𝐵 , 𝐵 , 𝐴 } = { 𝐵 , 𝐴 }
3		prcom	⊢ { 𝐵 , 𝐴 } = { 𝐴 , 𝐵 }
4	1 2 3	3eqtri	⊢ { 𝐴 , 𝐵 , 𝐵 } = { 𝐴 , 𝐵 }