Description: The Axiom of Union and its converse. A class is a set iff its union is a set. (Contributed by NM, 11-Nov-2003)
Ref | Expression | ||
---|---|---|---|
Assertion | uniexb | ⊢ ( 𝐴 ∈ V ↔ ∪ 𝐴 ∈ V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniexg | ⊢ ( 𝐴 ∈ V → ∪ 𝐴 ∈ V ) | |
2 | uniexr | ⊢ ( ∪ 𝐴 ∈ V → 𝐴 ∈ V ) | |
3 | 1 2 | impbii | ⊢ ( 𝐴 ∈ V ↔ ∪ 𝐴 ∈ V ) |