Theorem eqsstri

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 16-Jul-1995)

	Ref	Expression
Hypotheses	eqsstr.1	$$⊢A=B$$
	eqsstr.2	$$⊢B\subseteq C$$
Assertion	eqsstri	$$⊢A\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		eqsstr.1	$$⊢A=B$$
2		eqsstr.2	$$⊢B\subseteq C$$
3	1	sseq1i	$$⊢A\subseteq C\leftrightarrow B\subseteq C$$
4	2 3	mpbir	$$⊢A\subseteq C$$