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 C_ B
	3sstr3.2	|- A = C
	3sstr3.3	|- B = D
Assertion	3sstr3i	|- C C_ D

Proof

Step	Hyp	Ref	Expression
1		3sstr3.1	|- A C_ B
2		3sstr3.2	|- A = C
3		3sstr3.3	|- B = D
4	2 3	sseq12i	|- ( A C_ B <-> C C_ D )
5	1 4	mpbi	|- C C_ D