Metamath Proof Explorer

Theorem eluz2b3

Description: Two ways to say "an integer greater than or equal to 2". (Contributed by Paul Chapman, 23-Nov-2012)

Ref Expression
Assertion eluz2b3 ⊢ N ∈ ℤ ≥ 2 ↔ N ∈ ℕ ∧ N ≠ 1

Proof

Step Hyp Ref Expression
1 eluz2b2 ⊢ N ∈ ℤ ≥ 2 ↔ N ∈ ℕ ∧ 1 < N
2 nngt1ne1 ⊢ N ∈ ℕ → 1 < N ↔ N ≠ 1
3 2 pm5.32i ⊢ N ∈ ℕ ∧ 1 < N ↔ N ∈ ℕ ∧ N ≠ 1
4 1 3 bitri ⊢ N ∈ ℤ ≥ 2 ↔ N ∈ ℕ ∧ N ≠ 1