Theorem 0domg

Description: Any set dominates the empty set. (Contributed by NM, 26-Oct-2003) (Revised by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Assertion	0domg	⊢ ( 𝐴 ∈ 𝑉 → ∅ ≼ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		0ss	⊢ ∅ ⊆ 𝐴
2		ssdomg	⊢ ( 𝐴 ∈ 𝑉 → ( ∅ ⊆ 𝐴 → ∅ ≼ 𝐴 ) )
3	1 2	mpi	⊢ ( 𝐴 ∈ 𝑉 → ∅ ≼ 𝐴 )