Theorem sseqtrrd

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

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

Proof

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