**Description:** A positive real is nonzero. (Contributed by NM, 18-Jul-2008)

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

Assertion | rpne0 | $${\u22a2}{A}\in {\mathbb{R}}^{+}\to {A}\ne 0$$ |

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

1 | rpregt0 | $${\u22a2}{A}\in {\mathbb{R}}^{+}\to \left({A}\in \mathbb{R}\wedge 0<{A}\right)$$ | |

2 | gt0ne0 | $${\u22a2}\left({A}\in \mathbb{R}\wedge 0<{A}\right)\to {A}\ne 0$$ | |

3 | 1 2 | syl | $${\u22a2}{A}\in {\mathbb{R}}^{+}\to {A}\ne 0$$ |