**Description:** Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995)

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

Hypothesis | 3impb.1 | $${\u22a2}\left({\phi}\wedge \left({\psi}\wedge {\chi}\right)\right)\to {\theta}$$ | |

Assertion | 3impb | $${\u22a2}\left({\phi}\wedge {\psi}\wedge {\chi}\right)\to {\theta}$$ |

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

1 | 3impb.1 | $${\u22a2}\left({\phi}\wedge \left({\psi}\wedge {\chi}\right)\right)\to {\theta}$$ | |

2 | 1 | exp32 | $${\u22a2}{\phi}\to \left({\psi}\to \left({\chi}\to {\theta}\right)\right)$$ |

3 | 2 | 3imp | $${\u22a2}\left({\phi}\wedge {\psi}\wedge {\chi}\right)\to {\theta}$$ |