Theorem tpeq2d

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

	Ref	Expression
Hypothesis	tpeq1d.1	$$⊢\phi \to A=B$$
Assertion	tpeq2d	$$⊢\phi \to \left\{C,A,D\right\}=\left\{C,B,D\right\}$$

Proof

Step	Hyp	Ref	Expression
1		tpeq1d.1	$$⊢\phi \to A=B$$
2		tpeq2	$$⊢A=B\to \left\{C,A,D\right\}=\left\{C,B,D\right\}$$
3	1 2	syl	$$⊢\phi \to \left\{C,A,D\right\}=\left\{C,B,D\right\}$$