**Description:** Equality deduction for class intersection. (Contributed by NM, 2-Sep-2003)

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

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

Assertion | inteqd | $${\u22a2}{\phi}\to \bigcap {A}=\bigcap {B}$$ |

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

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

2 | inteq | $${\u22a2}{A}={B}\to \bigcap {A}=\bigcap {B}$$ | |

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