Theorem sseqtrrdi

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

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

Proof

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