Metamath Proof Explorer


Theorem nnzd

Description: A positive integer is an integer. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis nnzd.1 ⊢ ( 𝜑 → 𝐴 ∈ ℕ )
Assertion nnzd ( 𝜑 → 𝐴 ∈ ℤ )

Proof

Step Hyp Ref Expression
1 nnzd.1 ⊢ ( 𝜑 → 𝐴 ∈ ℕ )
2 1 nnnn0d ⊢ ( 𝜑 → 𝐴 ∈ ℕ0 )
3 2 nn0zd ⊢ ( 𝜑 → 𝐴 ∈ ℤ )