**Description:** Inference chaining two syllogisms syl . Inference associated with
imim12i . (Contributed by NM, 28-Dec-1992)

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

Hypotheses | 3syl.1 | $${\u22a2}{\phi}\to {\psi}$$ | |

3syl.2 | $${\u22a2}{\psi}\to {\chi}$$ | ||

3syl.3 | $${\u22a2}{\chi}\to {\theta}$$ | ||

Assertion | 3syl | $${\u22a2}{\phi}\to {\theta}$$ |

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

1 | 3syl.1 | $${\u22a2}{\phi}\to {\psi}$$ | |

2 | 3syl.2 | $${\u22a2}{\psi}\to {\chi}$$ | |

3 | 3syl.3 | $${\u22a2}{\chi}\to {\theta}$$ | |

4 | 1 2 | syl | $${\u22a2}{\phi}\to {\chi}$$ |

5 | 4 3 | syl | $${\u22a2}{\phi}\to {\theta}$$ |