**Description:** Equality deduction for intersection of two classes. (Contributed by NM, 10-Apr-1994)

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

Hypothesis | ineq1d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

Assertion | ineq1d | $${\u22a2}{\phi}\to {A}\cap {C}={B}\cap {C}$$ |

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

1 | ineq1d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

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

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