Theorem sseqtrid

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

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

Proof

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