Metamath Proof Explorer


Theorem zcnd

Description: An integer is a complex number. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis zred.1 ⊢ φ → A ∈ ℤ
Assertion zcnd ⊢ φ → A ∈ ℂ

Proof

Step Hyp Ref Expression
1 zred.1 ⊢ φ → A ∈ ℤ
2 1 zred ⊢ φ → A ∈ ℝ
3 2 recnd ⊢ φ → A ∈ ℂ