**Description:** Equality theorem for intersection of two classes. (Contributed by NM, 26-Dec-1993)

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

Assertion | ineq2 | $${\u22a2}{A}={B}\to {C}\cap {A}={C}\cap {B}$$ |

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

1 | ineq1 | $${\u22a2}{A}={B}\to {A}\cap {C}={B}\cap {C}$$ | |

2 | incom | $${\u22a2}{C}\cap {A}={A}\cap {C}$$ | |

3 | incom | $${\u22a2}{C}\cap {B}={B}\cap {C}$$ | |

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