Metamath Proof Explorer


Theorem 0le2

Description: The number 0 is less than or equal to 2. (Contributed by David A. Wheeler, 7-Dec-2018) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

Ref Expression
Assertion 0le2 ⊢ 0 ≤ 2

Proof

Step Hyp Ref Expression
1 0re ⊢ 0 ∈ ℝ
2 2re ⊢ 2 ∈ ℝ
3 2nn ⊢ 2 ∈ ℕ
4 3 nngt0i ⊢ 0 < 2
5 1 2 4 ltleii ⊢ 0 ≤ 2