This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem riotaclbBAD

Description: Closure of restricted iota. (Contributed by NM, 15-Sep-2011)

Ref Expression
Hypothesis riotaclb.1 ⊢ A ∈ V
Assertion riotaclbBAD ⊢ ∃! x ∈ A φ ↔ ι x ∈ A | φ ∈ A

Proof

Step Hyp Ref Expression
1 riotaclb.1 ⊢ A ∈ V
2 riotaclbgBAD ⊢ A ∈ V → ∃! x ∈ A φ ↔ ι x ∈ A | φ ∈ A
3 1 2 ax-mp ⊢ ∃! x ∈ A φ ↔ ι x ∈ A | φ ∈ A