**Description:** Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007)

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

Hypothesis | 3ad2antl.1 | $${\u22a2}\left({\phi}\wedge {\chi}\right)\to {\theta}$$ | |

Assertion | 3ad2antl2 | $${\u22a2}\left(\left({\psi}\wedge {\phi}\wedge {\tau}\right)\wedge {\chi}\right)\to {\theta}$$ |

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

1 | 3ad2antl.1 | $${\u22a2}\left({\phi}\wedge {\chi}\right)\to {\theta}$$ | |

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

3 | 2 | 3adantl1 | $${\u22a2}\left(\left({\psi}\wedge {\phi}\wedge {\tau}\right)\wedge {\chi}\right)\to {\theta}$$ |