Theorem eqsstrrd

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004)

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

Proof

Step	Hyp	Ref	Expression
1		eqsstrrd.1	|- ( ph -> B = A )
2		eqsstrrd.2	|- ( ph -> B C_ C )
3	1	eqcomd	|- ( ph -> A = B )
4	3 2	eqsstrd	|- ( ph -> A C_ C )