**Description:** Deduction of equality of two class unions. (Contributed by NM, 21-Apr-1995)

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

Hypothesis | unieqd.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

Assertion | unieqd | $${\u22a2}{\phi}\to \bigcup {A}=\bigcup {B}$$ |

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

1 | unieqd.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

2 | unieq | $${\u22a2}{A}={B}\to \bigcup {A}=\bigcup {B}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to \bigcup {A}=\bigcup {B}$$ |