**Description:** The first argument of a binary relation belongs to its domain.
(Contributed by NM, 28-Apr-2015)

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

Hypothesis | releldm.1 | $${\u22a2}\mathrm{Rel}{R}$$ | |

Assertion | releldmi | $${\u22a2}{A}{R}{B}\to {A}\in \mathrm{dom}{R}$$ |

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

1 | releldm.1 | $${\u22a2}\mathrm{Rel}{R}$$ | |

2 | releldm | $${\u22a2}\left(\mathrm{Rel}{R}\wedge {A}{R}{B}\right)\to {A}\in \mathrm{dom}{R}$$ | |

3 | 1 2 | mpan | $${\u22a2}{A}{R}{B}\to {A}\in \mathrm{dom}{R}$$ |