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

Metamath Proof Explorer

Theorem indisuni

Description: The base set of the indiscrete topology. (Contributed by Mario Carneiro, 14-Aug-2015)

Ref Expression
Assertion indisuni ⊢ I ⁡ A = ⋃ ∅ A

Proof

Step Hyp Ref Expression
1 indislem ⊢ ∅ I ⁡ A = ∅ A
2 fvex ⊢ I ⁡ A ∈ V
3 indistopon ⊢ I ⁡ A ∈ V → ∅ I ⁡ A ∈ TopOn ⁡ I ⁡ A
4 2 3 ax-mp ⊢ ∅ I ⁡ A ∈ TopOn ⁡ I ⁡ A
5 1 4 eqeltrri ⊢ ∅ A ∈ TopOn ⁡ I ⁡ A
6 5 toponunii ⊢ I ⁡ A = ⋃ ∅ A