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Metamath Proof Explorer

Theorem eluzelcn

Description: A member of an upper set of integers is a complex number. (Contributed by Glauco Siliprandi, 29-Jun-2017)

Ref Expression
Assertion eluzelcn ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝑁 ∈ ℂ )

Proof

Step Hyp Ref Expression
1 eluzelre ⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝑁 ∈ ℝ )
2 1 recnd ⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝑁 ∈ ℂ )