Theorem eqsstrrid

Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004)

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

Proof

Step	Hyp	Ref	Expression
1		eqsstrrid.1	$$⊢B=A$$
2		eqsstrrid.2	$$⊢\phi \to B\subseteq C$$
3	1	eqcomi	$$⊢A=B$$
4	3 2	eqsstrid	$$⊢\phi \to A\subseteq C$$