Metamath Proof Explorer

Theorem elinel1

Description: Membership in an intersection implies membership in the first set. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Assertion elinel1 
|- ( A e. ( B i^i C ) -> A e. B )

Proof

Step Hyp Ref Expression
1 elin 
 |-  ( A e. ( B i^i C ) <-> ( A e. B /\ A e. C ) )
2 1 simplbi 
 |-  ( A e. ( B i^i C ) -> A e. B )