**Description:** Closure law for negative of reals. (Contributed by Mario Carneiro, 27-May-2016)

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

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

Assertion | renegcld | $${\u22a2}{\phi}\to -{A}\in \mathbb{R}$$ |

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

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

2 | renegcl | $${\u22a2}{A}\in \mathbb{R}\to -{A}\in \mathbb{R}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to -{A}\in \mathbb{R}$$ |