Theorem 0sdom

Description: A set strictly dominates the empty set iff it is not empty. (Contributed by NM, 29-Jul-2004)

	Ref	Expression
Hypothesis	0sdom.1	⊢ 𝐴 ∈ V
Assertion	0sdom	⊢ ( ∅ ≺ 𝐴 ↔ 𝐴 ≠ ∅ )

Proof

Step	Hyp	Ref	Expression
1		0sdom.1	⊢ 𝐴 ∈ V
2		0sdomg	⊢ ( 𝐴 ∈ V → ( ∅ ≺ 𝐴 ↔ 𝐴 ≠ ∅ ) )
3	1 2	ax-mp	⊢ ( ∅ ≺ 𝐴 ↔ 𝐴 ≠ ∅ )