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Metamath Proof Explorer

Theorem zre

Description: An integer is a real. (Contributed by NM, 8-Jan-2002)

Ref Expression
Assertion zre ( 𝑁 ∈ ℤ → 𝑁 ∈ ℝ )

Proof

Step Hyp Ref Expression
1 elz ⊢ ( 𝑁 ∈ ℤ ↔ ( 𝑁 ∈ ℝ ∧ ( 𝑁 = 0 ∨ 𝑁 ∈ ℕ ∨ - 𝑁 ∈ ℕ ) ) )
2 1 simplbi ⊢ ( 𝑁 ∈ ℤ → 𝑁 ∈ ℝ )