Metamath Proof Explorer

Theorem eldm

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 )

Proof

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 )