Theorem sspsstrd

Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of sspsstr . (Contributed by David Moews, 1-May-2017)

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

Proof

Step	Hyp	Ref	Expression
1		sspsstrd.1	|- ( ph -> A C_ B )
2		sspsstrd.2	|- ( ph -> B C. C )
3		sspsstr	|- ( ( A C_ B /\ B C. C ) -> A C. C )
4	1 2 3	syl2anc	|- ( ph -> A C. C )