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

Ref | Expression | ||
---|---|---|---|

Hypothesis | crred.1 | $${\u22a2}{\phi}\to {A}\in \mathbb{R}$$ | |

Assertion | reim0d | $${\u22a2}{\phi}\to \Im \left({A}\right)=0$$ |

Step | Hyp | Ref | Expression |
---|---|---|---|

1 | crred.1 | $${\u22a2}{\phi}\to {A}\in \mathbb{R}$$ | |

2 | reim0 | $${\u22a2}{A}\in \mathbb{R}\to \Im \left({A}\right)=0$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to \Im \left({A}\right)=0$$ |