Theorem 3sstr4i

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	3sstr4.1	$$⊢A\subseteq B$$
	3sstr4.2	$$⊢C=A$$
	3sstr4.3	$$⊢D=B$$
Assertion	3sstr4i	$$⊢C\subseteq D$$

Proof

Step	Hyp	Ref	Expression
1		3sstr4.1	$$⊢A\subseteq B$$
2		3sstr4.2	$$⊢C=A$$
3		3sstr4.3	$$⊢D=B$$
4	2 3	sseq12i	$$⊢C\subseteq D\leftrightarrow A\subseteq B$$
5	1 4	mpbir	$$⊢C\subseteq D$$