Theorem sstrdi

Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

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

Proof

Step	Hyp	Ref	Expression
1		sstrdi.1	|- ( ph -> A C_ B )
2		sstrdi.2	|- B C_ C
3	2	a1i	|- ( ph -> B C_ C )
4	1 3	sstrd	|- ( ph -> A C_ C )