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

Ref | Expression | ||
---|---|---|---|

Assertion | elinel2 | $${\u22a2}{A}\in \left({B}\cap {C}\right)\to {A}\in {C}$$ |

Step | Hyp | Ref | Expression |
---|---|---|---|

1 | elin | $${\u22a2}{A}\in \left({B}\cap {C}\right)\leftrightarrow \left({A}\in {B}\wedge {A}\in {C}\right)$$ | |

2 | 1 | simprbi | $${\u22a2}{A}\in \left({B}\cap {C}\right)\to {A}\in {C}$$ |