Theorem tpeq1d

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

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

Proof

Step	Hyp	Ref	Expression
1		tpeq1d.1	$$⊢\phi \to A=B$$
2		tpeq1	$$⊢A=B\to \left\{A,C,D\right\}=\left\{B,C,D\right\}$$
3	1 2	syl	$$⊢\phi \to \left\{A,C,D\right\}=\left\{B,C,D\right\}$$