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	$$⊢\left\{A,B,B\right\}=\left\{A,B\right\}$$

Proof

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