Theorem 3sstr4d

Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 30-Nov-1995) (Proof shortened by Eric Schmidt, 26-Jan-2007)

	Ref	Expression
Hypotheses	3sstr4d.1	|- ( ph -> A C_ B )
	3sstr4d.2	|- ( ph -> C = A )
	3sstr4d.3	|- ( ph -> D = B )
Assertion	3sstr4d	|- ( ph -> C C_ D )

Proof

Step	Hyp	Ref	Expression
1		3sstr4d.1	|- ( ph -> A C_ B )
2		3sstr4d.2	|- ( ph -> C = A )
3		3sstr4d.3	|- ( ph -> D = B )
4	2 1	eqsstrd	|- ( ph -> C C_ B )
5	4 3	sseqtrrd	|- ( ph -> C C_ D )