Theorem ssinss1d

Description: Intersection preserves subclass relationship. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypothesis	ssinss1d.1	|- ( ph -> A C_ C )
Assertion	ssinss1d	|- ( ph -> ( A i^i B ) C_ C )

Proof

Step	Hyp	Ref	Expression
1		ssinss1d.1	|- ( ph -> A C_ C )
2		ssinss1	|- ( A C_ C -> ( A i^i B ) C_ C )
3	1 2	syl	|- ( ph -> ( A i^i B ) C_ C )