Metamath Proof Explorer


Theorem replimi

Description: Construct a complex number from its real and imaginary parts. (Contributed by NM, 1-Oct-1999)

Ref Expression
Hypothesis recl.1 ⊢ A ∈ ℂ
Assertion replimi ⊢ A = ℜ ⁡ A + i ⁢ ℑ ⁡ A

Proof

Step Hyp Ref Expression
1 recl.1 ⊢ A ∈ ℂ
2 replim ⊢ A ∈ ℂ → A = ℜ ⁡ A + i ⁢ ℑ ⁡ A
3 1 2 ax-mp ⊢ A = ℜ ⁡ A + i ⁢ ℑ ⁡ A