Theorem 3sstr3i

Description: Substitution of equality in both sides of a subclass relationship. (Contributed by NM, 13-Jan-1996) (Proof shortened by Eric Schmidt, 26-Jan-2007)

	Ref	Expression
Hypotheses	3sstr3.1	$$⊢A\subseteq B$$
	3sstr3.2	$$⊢A=C$$
	3sstr3.3	$$⊢B=D$$
Assertion	3sstr3i	$$⊢C\subseteq D$$

Proof

Step	Hyp	Ref	Expression
1		3sstr3.1	$$⊢A\subseteq B$$
2		3sstr3.2	$$⊢A=C$$
3		3sstr3.3	$$⊢B=D$$
4	2 3	sseq12i	$$⊢A\subseteq B\leftrightarrow C\subseteq D$$
5	1 4	mpbi	$$⊢C\subseteq D$$