Theorem psstrd

Description: Proper subclass inclusion is transitive. Deduction form of psstr . (Contributed by David Moews, 1-May-2017)

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

Proof

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