Theorem ssrind

Description: Add right intersection to subclass relation. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	ssrind.1	|- ( ph -> A C_ B )
Assertion	ssrind	|- ( ph -> ( A i^i C ) C_ ( B i^i C ) )

Proof

Step	Hyp	Ref	Expression
1		ssrind.1	|- ( ph -> A C_ B )
2		ssrin	|- ( A C_ B -> ( A i^i C ) C_ ( B i^i C ) )
3	1 2	syl	|- ( ph -> ( A i^i C ) C_ ( B i^i C ) )