Theorem renegd

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

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

Proof

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