**Description:** A mixed syllogism inference from an implication and a biconditional.
(Contributed by NM, 3-Jan-1993)

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

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

sylib.2 | $${\u22a2}{\psi}\leftrightarrow {\chi}$$ | ||

Assertion | sylib | $${\u22a2}{\phi}\to {\chi}$$ |

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

1 | sylib.1 | $${\u22a2}{\phi}\to {\psi}$$ | |

2 | sylib.2 | $${\u22a2}{\psi}\leftrightarrow {\chi}$$ | |

3 | 2 | biimpi | $${\u22a2}{\psi}\to {\chi}$$ |

4 | 1 3 | syl | $${\u22a2}{\phi}\to {\chi}$$ |