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

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

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

Assertion | negcld | $${\u22a2}{\phi}\to -{A}\in \u2102$$ |

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

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

2 | negcl | $${\u22a2}{A}\in \u2102\to -{A}\in \u2102$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to -{A}\in \u2102$$ |