Theorem sselid

Description: Membership inference from subclass relationship. (Contributed by NM, 25-Jun-2014)

	Ref	Expression
Hypotheses	sseli.1	|- A C_ B
	sselid.2	|- ( ph -> C e. A )
Assertion	sselid	|- ( ph -> C e. B )

Proof

Step	Hyp	Ref	Expression
1		sseli.1	|- A C_ B
2		sselid.2	|- ( ph -> C e. A )
3	1	sseli	|- ( C e. A -> C e. B )
4	2 3	syl	|- ( ph -> C e. B )