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

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

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

readdcld.2 | $${\u22a2}{\phi}\to {B}\in \mathbb{R}$$ | ||

Assertion | remulcld | $${\u22a2}{\phi}\to {A}{B}\in \mathbb{R}$$ |

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

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

2 | readdcld.2 | $${\u22a2}{\phi}\to {B}\in \mathbb{R}$$ | |

3 | remulcl | $${\u22a2}\left({A}\in \mathbb{R}\wedge {B}\in \mathbb{R}\right)\to {A}{B}\in \mathbb{R}$$ | |

4 | 1 2 3 | syl2anc | $${\u22a2}{\phi}\to {A}{B}\in \mathbb{R}$$ |