Theorem tpeq3d

Description: Equality theorem for unordered triples. (Contributed by NM, 22-Jun-2014)

	Ref	Expression
Hypothesis	tpeq1d.1	$$⊢\phi \to A=B$$
Assertion	tpeq3d	$$⊢\phi \to \left\{C,D,A\right\}=\left\{C,D,B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		tpeq1d.1	$$⊢\phi \to A=B$$
2		tpeq3	$$⊢A=B\to \left\{C,D,A\right\}=\left\{C,D,B\right\}$$
3	1 2	syl	$$⊢\phi \to \left\{C,D,A\right\}=\left\{C,D,B\right\}$$