Theorem sseqtrdi

Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004)

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

Proof

Step	Hyp	Ref	Expression
1		sseqtrdi.1	|- ( ph -> A C_ B )
2		sseqtrdi.2	|- B = C
3	2	sseq2i	|- ( A C_ B <-> A C_ C )
4	1 3	sylib	|- ( ph -> A C_ C )