**Description:** A set equals the union of its singleton. Theorem 8.2 of Quine p. 53.
(Contributed by NM, 30-Aug-1993)

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

Hypothesis | unisn.1 | $${\u22a2}{A}\in \mathrm{V}$$ | |

Assertion | unisn | $${\u22a2}\bigcup \left\{{A}\right\}={A}$$ |

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

1 | unisn.1 | $${\u22a2}{A}\in \mathrm{V}$$ | |

2 | unisng | $${\u22a2}{A}\in \mathrm{V}\to \bigcup \left\{{A}\right\}={A}$$ | |

3 | 1 2 | ax-mp | $${\u22a2}\bigcup \left\{{A}\right\}={A}$$ |