Theorem cjnegd

Description: Complex conjugate of negative. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	recld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	cjnegd	⊢ ( 𝜑 → ( ∗ ‘ - 𝐴 ) = - ( ∗ ‘ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		recld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		cjneg	⊢ ( 𝐴 ∈ ℂ → ( ∗ ‘ - 𝐴 ) = - ( ∗ ‘ 𝐴 ) )
3	1 2	syl	⊢ ( 𝜑 → ( ∗ ‘ - 𝐴 ) = - ( ∗ ‘ 𝐴 ) )