**Description:** An element of a class is a subclass of its union. Theorem 8.6 of Quine
p. 54. Also the basis for Proposition 7.20 of TakeutiZaring p. 40.
(Contributed by NM, 6-Jun-1994)

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

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

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

1 | ssid | $${\u22a2}{A}\subseteq {A}$$ | |

2 | ssuni | $${\u22a2}\left({A}\subseteq {A}\wedge {A}\in {B}\right)\to {A}\subseteq \bigcup {B}$$ | |

3 | 1 2 | mpan | $${\u22a2}{A}\in {B}\to {A}\subseteq \bigcup {B}$$ |