Theorem sseqtri

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 28-Jul-1995)

	Ref	Expression
Hypotheses	sseqtr.1	|- A C_ B
	sseqtr.2	|- B = C
Assertion	sseqtri	|- A C_ C

Proof

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