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 ) |
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 ) |