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

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

Hypotheses | sylbi.1 | $${\u22a2}{\phi}\leftrightarrow {\psi}$$ | |

sylbi.2 | $${\u22a2}{\psi}\to {\chi}$$ | ||

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

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

1 | sylbi.1 | $${\u22a2}{\phi}\leftrightarrow {\psi}$$ | |

2 | sylbi.2 | $${\u22a2}{\psi}\to {\chi}$$ | |

3 | 1 | biimpi | $${\u22a2}{\phi}\to {\psi}$$ |

4 | 3 2 | syl | $${\u22a2}{\phi}\to {\chi}$$ |