Theorem imnegi

Description: Imaginary part of negative. (Contributed by NM, 2-Aug-1999)

	Ref	Expression
Hypothesis	recl.1	⊢ 𝐴 ∈ ℂ
Assertion	imnegi	⊢ ( ℑ ‘ - 𝐴 ) = - ( ℑ ‘ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		recl.1	⊢ 𝐴 ∈ ℂ
2		imneg	⊢ ( 𝐴 ∈ ℂ → ( ℑ ‘ - 𝐴 ) = - ( ℑ ‘ 𝐴 ) )
3	1 2	ax-mp	⊢ ( ℑ ‘ - 𝐴 ) = - ( ℑ ‘ 𝐴 )