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