Description: Membership in a domain. Theorem 4 of Suppes p. 59. (Contributed by NM, 2-Apr-2004)
Ref | Expression | ||
---|---|---|---|
Hypothesis | eldm.1 | |- A e. _V |
|
Assertion | eldm | |- ( A e. dom B <-> E. y A B y ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldm.1 | |- A e. _V |
|
2 | eldmg | |- ( A e. _V -> ( A e. dom B <-> E. y A B y ) ) |
|
3 | 1 2 | ax-mp | |- ( A e. dom B <-> E. y A B y ) |