Theorem sseqtri

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 28-Jul-1995)

	Ref	Expression
Hypotheses	sseqtr.1	$$⊢A\subseteq B$$
	sseqtr.2	$$⊢B=C$$
Assertion	sseqtri	$$⊢A\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		sseqtr.1	$$⊢A\subseteq B$$
2		sseqtr.2	$$⊢B=C$$
3	2	sseq2i	$$⊢A\subseteq B\leftrightarrow A\subseteq C$$
4	1 3	mpbi	$$⊢A\subseteq C$$