Theorem nel2nelini

Description: Membership in an intersection implies membership in the second set. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	nel2nelini.1	|- -. A e. C
Assertion	nel2nelini	|- -. A e. ( B i^i C )

Proof

Step	Hyp	Ref	Expression
1		nel2nelini.1	|- -. A e. C
2		nel2nelin	|- ( -. A e. C -> -. A e. ( B i^i C ) )
3	1 2	ax-mp	|- -. A e. ( B i^i C )