**Description:** Deduction adding union to the right in a class equality. (Contributed by NM, 29-Mar-1998)

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

Hypothesis | uneq1d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

Assertion | uneq1d | $${\u22a2}{\phi}\to {A}\cup {C}={B}\cup {C}$$ |

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

1 | uneq1d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

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

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