Theorem reim0d

Description: The imaginary part of a real number is 0. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	crred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	reim0d	⊢ ( 𝜑 → ( ℑ ‘ 𝐴 ) = 0 )

Proof

Step	Hyp	Ref	Expression
1		crred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		reim0	⊢ ( 𝐴 ∈ ℝ → ( ℑ ‘ 𝐴 ) = 0 )
3	1 2	syl	⊢ ( 𝜑 → ( ℑ ‘ 𝐴 ) = 0 )