**Description:** Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011)

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

Assertion | simp11 | $${\u22a2}\left(\left({\phi}\wedge {\psi}\wedge {\chi}\right)\wedge {\theta}\wedge {\tau}\right)\to {\phi}$$ |

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

1 | simp1 | $${\u22a2}\left({\phi}\wedge {\psi}\wedge {\chi}\right)\to {\phi}$$ | |

2 | 1 | 3ad2ant1 | $${\u22a2}\left(\left({\phi}\wedge {\psi}\wedge {\chi}\right)\wedge {\theta}\wedge {\tau}\right)\to {\phi}$$ |