**Description:** A real number is less than or equal to its absolute value. (Contributed by Mario Carneiro, 29-May-2016)

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

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

Assertion | leabsd | $${\u22a2}{\phi}\to {A}\le \left|{A}\right|$$ |

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

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

2 | leabs | $${\u22a2}{A}\in \mathbb{R}\to {A}\le \left|{A}\right|$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to {A}\le \left|{A}\right|$$ |