Theorem sseqtrd

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

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

Proof

Step	Hyp	Ref	Expression
1		sseqtrd.1	|- ( ph -> A C_ B )
2		sseqtrd.2	|- ( ph -> B = C )
3	2	sseq2d	|- ( ph -> ( A C_ B <-> A C_ C ) )
4	1 3	mpbid	|- ( ph -> A C_ C )