Theorem sylan9ssr

Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004)

	Ref	Expression
Hypotheses	sylan9ssr.1	|- ( ph -> A C_ B )
	sylan9ssr.2	|- ( ps -> B C_ C )
Assertion	sylan9ssr	|- ( ( ps /\ ph ) -> A C_ C )

Proof

Step	Hyp	Ref	Expression
1		sylan9ssr.1	|- ( ph -> A C_ B )
2		sylan9ssr.2	|- ( ps -> B C_ C )
3	1 2	sylan9ss	|- ( ( ph /\ ps ) -> A C_ C )
4	3	ancoms	|- ( ( ps /\ ph ) -> A C_ C )