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Metamath Proof Explorer

Theorem cnfldxms

Description: The complex number field is a topological space. (Contributed by Mario Carneiro, 28-Aug-2015)

Ref Expression
Assertion cnfldxms ⊢ ℂ fld ∈ ∞MetSp

Proof

Step Hyp Ref Expression
1 cnfldms ⊢ ℂ fld ∈ MetSp
2 msxms ⊢ ℂ fld ∈ MetSp → ℂ fld ∈ ∞MetSp
3 1 2 ax-mp ⊢ ℂ fld ∈ ∞MetSp