Theorem 3sstr3g

Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 1-Oct-2000)

	Ref	Expression
Hypotheses	3sstr3g.1	|- ( ph -> A C_ B )
	3sstr3g.2	|- A = C
	3sstr3g.3	|- B = D
Assertion	3sstr3g	|- ( ph -> C C_ D )

Proof

Step	Hyp	Ref	Expression
1		3sstr3g.1	|- ( ph -> A C_ B )
2		3sstr3g.2	|- A = C
3		3sstr3g.3	|- B = D
4	2 3	sseq12i	|- ( A C_ B <-> C C_ D )
5	1 4	sylib	|- ( ph -> C C_ D )