**Description:** Deduction adding conjuncts to an antecedent. (Contributed by NM, 21-Apr-2005)

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

Hypothesis | 3ad2ant.1 | $${\u22a2}{\phi}\to {\chi}$$ | |

Assertion | 3ad2ant1 | $${\u22a2}\left({\phi}\wedge {\psi}\wedge {\theta}\right)\to {\chi}$$ |

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

1 | 3ad2ant.1 | $${\u22a2}{\phi}\to {\chi}$$ | |

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

3 | 2 | 3adant2 | $${\u22a2}\left({\phi}\wedge {\psi}\wedge {\theta}\right)\to {\chi}$$ |