**Description:** Conjunction form of e02 . (Contributed by Alan Sare, 15-Jun-2011)
(Proof modification is discouraged.) (New usage is discouraged.)

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

Hypotheses | e02an.1 | $${\u22a2}{\phi}$$ | |

e02an.2 | $${\u22a2}\left({\psi}{,}{\chi}{\to}{\theta}\right)$$ | ||

e02an.3 | $${\u22a2}\left({\phi}\wedge {\theta}\right)\to {\tau}$$ | ||

Assertion | e02an | $${\u22a2}\left({\psi}{,}{\chi}{\to}{\tau}\right)$$ |

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

1 | e02an.1 | $${\u22a2}{\phi}$$ | |

2 | e02an.2 | $${\u22a2}\left({\psi}{,}{\chi}{\to}{\theta}\right)$$ | |

3 | e02an.3 | $${\u22a2}\left({\phi}\wedge {\theta}\right)\to {\tau}$$ | |

4 | 3 | ex | $${\u22a2}{\phi}\to \left({\theta}\to {\tau}\right)$$ |

5 | 1 2 4 | e02 | $${\u22a2}\left({\psi}{,}{\chi}{\to}{\tau}\right)$$ |