**Description:** No (finite) real equals plus infinity. (Contributed by Mario Carneiro, 28-May-2016)

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

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

Assertion | renepnfd | $${\u22a2}{\phi}\to {A}\ne \mathrm{+\infty}$$ |

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

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

2 | renepnf | $${\u22a2}{A}\in \mathbb{R}\to {A}\ne \mathrm{+\infty}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to {A}\ne \mathrm{+\infty}$$ |