Metamath Proof Explorer

Theorem mstps

Description: A metric space is a topological space. (Contributed by Mario Carneiro, 26-Aug-2015)

Ref Expression
Assertion mstps ⊢ M ∈ MetSp → M ∈ TopSp

Proof

Step Hyp Ref Expression
1 msxms ⊢ M ∈ MetSp → M ∈ ∞MetSp
2 xmstps ⊢ M ∈ ∞MetSp → M ∈ TopSp
3 1 2 syl ⊢ M ∈ MetSp → M ∈ TopSp