Theorem nel1nelini

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

	Ref	Expression
Hypothesis	nel1nelini.1	|- -. A e. B
Assertion	nel1nelini	|- -. A e. ( B i^i C )

Proof

Step	Hyp	Ref	Expression
1		nel1nelini.1	|- -. A e. B
2		nel1nelin	|- ( -. A e. B -> -. A e. ( B i^i C ) )
3	1 2	ax-mp	|- -. A e. ( B i^i C )