Theorem eqeltrrd

Description: Deduction that substitutes equal classes into membership. (Contributed by NM, 14-Dec-2004)

	Ref	Expression
Hypotheses	eqeltrrd.1	$$⊢\phi \to A=B$$
	eqeltrrd.2	$$⊢\phi \to A\in C$$
Assertion	eqeltrrd	$$⊢\phi \to B\in C$$

Proof

Step	Hyp	Ref	Expression
1		eqeltrrd.1	$$⊢\phi \to A=B$$
2		eqeltrrd.2	$$⊢\phi \to A\in C$$
3	1	eqcomd	$$⊢\phi \to B=A$$
4	3 2	eqeltrd	$$⊢\phi \to B\in C$$