**Description:** A chained equality inference for a binary relation. (Contributed by NM, 24-Apr-2005)

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

Hypotheses | breqtrrid.1 | $${\u22a2}{A}{R}{B}$$ | |

breqtrrid.2 | $${\u22a2}{\phi}\to {C}={B}$$ | ||

Assertion | breqtrrid | $${\u22a2}{\phi}\to {A}{R}{C}$$ |

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

1 | breqtrrid.1 | $${\u22a2}{A}{R}{B}$$ | |

2 | breqtrrid.2 | $${\u22a2}{\phi}\to {C}={B}$$ | |

3 | 2 | eqcomd | $${\u22a2}{\phi}\to {B}={C}$$ |

4 | 1 3 | breqtrid | $${\u22a2}{\phi}\to {A}{R}{C}$$ |