Theorem psssstrd

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

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

Proof

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