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Metamath Proof Explorer

Theorem imcji

Description: Imaginary part of a complex conjugate. (Contributed by NM, 2-Oct-1999)

Ref Expression
Hypothesis recl.1 ⊢ A ∈ ℂ
Assertion imcji ⊢ ℑ ⁡ A ‾ = − ℑ ⁡ A

Proof

Step Hyp Ref Expression
1 recl.1 ⊢ A ∈ ℂ
2 imcj ⊢ A ∈ ℂ → ℑ ⁡ A ‾ = − ℑ ⁡ A
3 1 2 ax-mp ⊢ ℑ ⁡ A ‾ = − ℑ ⁡ A