Metamath Proof Explorer


Theorem nn0cnd

Description: A nonnegative integer is a complex number. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis nn0red.1 ⊢ φ → A ∈ ℕ 0
Assertion nn0cnd ⊢ φ → A ∈ ℂ

Proof

Step Hyp Ref Expression
1 nn0red.1 ⊢ φ → A ∈ ℕ 0
2 1 nn0red ⊢ φ → A ∈ ℝ
3 2 recnd ⊢ φ → A ∈ ℂ