Metamath Proof Explorer


Theorem 3re

Description: The number 3 is real. (Contributed by NM, 27-May-1999)

Ref Expression
Assertion 3re ⊢ 3 ∈ ℝ

Proof

Step Hyp Ref Expression
1 df-3 ⊢ 3 = 2 + 1
2 2re ⊢ 2 ∈ ℝ
3 1re ⊢ 1 ∈ ℝ
4 2 3 readdcli ⊢ 2 + 1 ∈ ℝ
5 1 4 eqeltri ⊢ 3 ∈ ℝ