Theorem ssinss2d

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

	Ref	Expression
Hypothesis	ssinss2d.1	|- ( ph -> B C_ C )
Assertion	ssinss2d	|- ( ph -> ( A i^i B ) C_ C )

Proof

Step	Hyp	Ref	Expression
1		ssinss2d.1	|- ( ph -> B C_ C )
2		incom	|- ( A i^i B ) = ( B i^i A )
3	1	ssinss1d	|- ( ph -> ( B i^i A ) C_ C )
4	2 3	eqsstrid	|- ( ph -> ( A i^i B ) C_ C )