Metamath Proof Explorer


Theorem recli

Description: The real part of a complex number is real (closure law). (Contributed by NM, 11-May-1999)

Ref Expression
Hypothesis recl.1 ⊢ A ∈ ℂ
Assertion recli ⊢ ℜ ⁡ A ∈ ℝ

Proof

Step Hyp Ref Expression
1 recl.1 ⊢ A ∈ ℂ
2 recl ⊢ A ∈ ℂ → ℜ ⁡ A ∈ ℝ
3 1 2 ax-mp ⊢ ℜ ⁡ A ∈ ℝ