Theorem eqsstrd

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

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

Proof

Step	Hyp	Ref	Expression
1		eqsstrd.1	|- ( ph -> A = B )
2		eqsstrd.2	|- ( ph -> B C_ C )
3	1	sseq1d	|- ( ph -> ( A C_ C <-> B C_ C ) )
4	2 3	mpbird	|- ( ph -> A C_ C )