Metamath Proof Explorer


Theorem re0

Description: The real part of zero. (Contributed by NM, 27-Jul-1999)

Ref Expression
Assertion re0 ⊢ ℜ ⁡ 0 = 0

Proof

Step Hyp Ref Expression
1 0re ⊢ 0 ∈ ℝ
2 rere ⊢ 0 ∈ ℝ → ℜ ⁡ 0 = 0
3 1 2 ax-mp ⊢ ℜ ⁡ 0 = 0