**Description:** An equality transitivity equality deduction. (Contributed by NM, 18-Jul-1995)

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

Hypotheses | eqtr3d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

eqtr3d.2 | $${\u22a2}{\phi}\to {A}={C}$$ | ||

Assertion | eqtr3d | $${\u22a2}{\phi}\to {B}={C}$$ |

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

1 | eqtr3d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

2 | eqtr3d.2 | $${\u22a2}{\phi}\to {A}={C}$$ | |

3 | 1 | eqcomd | $${\u22a2}{\phi}\to {B}={A}$$ |

4 | 3 2 | eqtrd | $${\u22a2}{\phi}\to {B}={C}$$ |