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

Proof

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