Theorem eqsstrdi

Description: A chained subclass and equality deduction. (Contributed by Mario Carneiro, 2-Jan-2017)

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

Proof

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