Theorem eqsstrrd

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004)

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

Proof

Step	Hyp	Ref	Expression
1		eqsstrrd.1	$$⊢\phi \to B=A$$
2		eqsstrrd.2	$$⊢\phi \to B\subseteq C$$
3	1	eqcomd	$$⊢\phi \to A=B$$
4	3 2	eqsstrd	$$⊢\phi \to A\subseteq C$$