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

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

Hypothesis | recld.1 | $${\u22a2}{\phi}\to {A}\in \u2102$$ | |

Assertion | imcld | $${\u22a2}{\phi}\to \Im \left({A}\right)\in \mathbb{R}$$ |

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

1 | recld.1 | $${\u22a2}{\phi}\to {A}\in \u2102$$ | |

2 | imcl | $${\u22a2}{A}\in \u2102\to \Im \left({A}\right)\in \mathbb{R}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to \Im \left({A}\right)\in \mathbb{R}$$ |