Theorem 3sstr4g

Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 16-Aug-1994) (Proof shortened by Eric Schmidt, 26-Jan-2007)

	Ref	Expression
Hypotheses	3sstr4g.1	|- ( ph -> A C_ B )
	3sstr4g.2	|- C = A
	3sstr4g.3	|- D = B
Assertion	3sstr4g	|- ( ph -> C C_ D )

Proof

Step	Hyp	Ref	Expression
1		3sstr4g.1	|- ( ph -> A C_ B )
2		3sstr4g.2	|- C = A
3		3sstr4g.3	|- D = B
4	2 3	sseq12i	|- ( C C_ D <-> A C_ B )
5	1 4	sylibr	|- ( ph -> C C_ D )