Metamath Proof Explorer

Theorem dfdm6

Description: Alternate definition of domain. (Contributed by Peter Mazsa, 2-Mar-2018)

Ref Expression
Assertion dfdm6 
|- dom R = { x | [ x ] R =/= (/) }

Proof

Step Hyp Ref Expression
1 ecdmn0 
 |-  ( x e. dom R <-> [ x ] R =/= (/) )
2 1 eqabi 
 |-  dom R = { x | [ x ] R =/= (/) }