Theorem sseqtrrid

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

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

Proof

Step	Hyp	Ref	Expression
1		sseqtrrid.1	|- B C_ A
2		sseqtrrid.2	|- ( ph -> C = A )
3	2	eqcomd	|- ( ph -> A = C )
4	1 3	sseqtrid	|- ( ph -> B C_ C )