Theorem eqsstrid

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

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

Proof

Step	Hyp	Ref	Expression
1		eqsstrid.1	$$⊢A=B$$
2		eqsstrid.2	$$⊢\phi \to B\subseteq C$$
3	1	sseq1i	$$⊢A\subseteq C\leftrightarrow B\subseteq C$$
4	2 3	sylibr	$$⊢\phi \to A\subseteq C$$