**Description:** A member of an ordinal number is a subset of it. (Contributed by NM, 11-Aug-1994)

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

Hypothesis | on.1 | $${\u22a2}{A}\in \mathrm{On}$$ | |

Assertion | onelssi | $${\u22a2}{B}\in {A}\to {B}\subseteq {A}$$ |

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

1 | on.1 | $${\u22a2}{A}\in \mathrm{On}$$ | |

2 | onelss | $${\u22a2}{A}\in \mathrm{On}\to \left({B}\in {A}\to {B}\subseteq {A}\right)$$ | |

3 | 1 2 | ax-mp | $${\u22a2}{B}\in {A}\to {B}\subseteq {A}$$ |