Description: The intersection of a nonempty class abstraction exists. (Contributed by NM, 21-Oct-2003)
Ref | Expression | ||
---|---|---|---|
Assertion | intexab | ⊢ ( ∃ 𝑥 𝜑 ↔ ∩ { 𝑥 ∣ 𝜑 } ∈ V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abn0 | ⊢ ( { 𝑥 ∣ 𝜑 } ≠ ∅ ↔ ∃ 𝑥 𝜑 ) | |
2 | intex | ⊢ ( { 𝑥 ∣ 𝜑 } ≠ ∅ ↔ ∩ { 𝑥 ∣ 𝜑 } ∈ V ) | |
3 | 1 2 | bitr3i | ⊢ ( ∃ 𝑥 𝜑 ↔ ∩ { 𝑥 ∣ 𝜑 } ∈ V ) |