Theorem reim0d

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

	Ref	Expression
Hypothesis	crred.1	$$⊢\phi \to A\in ℝ$$
Assertion	reim0d	$$⊢\phi \to \Im \left(A\right)=0$$

Proof

Step	Hyp	Ref	Expression
1		crred.1	$$⊢\phi \to A\in ℝ$$
2		reim0	$$⊢A\in ℝ\to \Im \left(A\right)=0$$
3	1 2	syl	$$⊢\phi \to \Im \left(A\right)=0$$