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Metamath Proof Explorer

Theorem cnxmet

Description: The absolute value metric is an extended metric. (Contributed by Mario Carneiro, 28-Aug-2015)

Ref Expression
Assertion cnxmet ⊢ abs ∘ − ∈ ∞Met ⁡ ℂ

Proof

Step Hyp Ref Expression
1 cnmet ⊢ abs ∘ − ∈ Met ⁡ ℂ
2 metxmet ⊢ abs ∘ − ∈ Met ⁡ ℂ → abs ∘ − ∈ ∞Met ⁡ ℂ
3 1 2 ax-mp ⊢ abs ∘ − ∈ ∞Met ⁡ ℂ