Theorem 3sstr3d

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

	Ref	Expression
Hypotheses	3sstr3d.1	|- ( ph -> A C_ B )
	3sstr3d.2	|- ( ph -> A = C )
	3sstr3d.3	|- ( ph -> B = D )
Assertion	3sstr3d	|- ( ph -> C C_ D )

Proof

Step	Hyp	Ref	Expression
1		3sstr3d.1	|- ( ph -> A C_ B )
2		3sstr3d.2	|- ( ph -> A = C )
3		3sstr3d.3	|- ( ph -> B = D )
4	2 3	sseq12d	|- ( ph -> ( A C_ B <-> C C_ D ) )
5	1 4	mpbid	|- ( ph -> C C_ D )