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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 ∈ dom ⁡ R ↔ x R ≠ ∅
2 1 eqabi ⊢ dom ⁡ R = x | x R ≠ ∅