Description: Closure of restricted iota. (Contributed by NM, 15-Sep-2011)
Ref | Expression | ||
---|---|---|---|
Hypothesis | riotaclb.1 | ⊢ 𝐴 ∈ V | |
Assertion | riotaclbBAD | ⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 ↔ ( ℩ 𝑥 ∈ 𝐴 𝜑 ) ∈ 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | riotaclb.1 | ⊢ 𝐴 ∈ V | |
2 | riotaclbgBAD | ⊢ ( 𝐴 ∈ V → ( ∃! 𝑥 ∈ 𝐴 𝜑 ↔ ( ℩ 𝑥 ∈ 𝐴 𝜑 ) ∈ 𝐴 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 ↔ ( ℩ 𝑥 ∈ 𝐴 𝜑 ) ∈ 𝐴 ) |