**Description:** Contrapositive inference for inequality. (Contributed by NM, 1-Apr-2007)

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

Hypothesis | necon2bi.1 | $${\u22a2}{\phi}\to {A}\ne {B}$$ | |

Assertion | necon2bi | $${\u22a2}{A}={B}\to \neg {\phi}$$ |

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

1 | necon2bi.1 | $${\u22a2}{\phi}\to {A}\ne {B}$$ | |

2 | 1 | neneqd | $${\u22a2}{\phi}\to \neg {A}={B}$$ |

3 | 2 | con2i | $${\u22a2}{A}={B}\to \neg {\phi}$$ |