**Description:** Equality theorem for the union of two classes. (Contributed by NM, 5-Aug-1993)

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

Assertion | uneq2 | $${\u22a2}{A}={B}\to {C}\cup {A}={C}\cup {B}$$ |

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

1 | uneq1 | $${\u22a2}{A}={B}\to {A}\cup {C}={B}\cup {C}$$ | |

2 | uncom | $${\u22a2}{C}\cup {A}={A}\cup {C}$$ | |

3 | uncom | $${\u22a2}{C}\cup {B}={B}\cup {C}$$ | |

4 | 1 2 3 | 3eqtr4g | $${\u22a2}{A}={B}\to {C}\cup {A}={C}\cup {B}$$ |