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

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

Hypotheses | eqtr4d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

eqtr4d.2 | $${\u22a2}{\phi}\to {C}={B}$$ | ||

Assertion | eqtr4d | $${\u22a2}{\phi}\to {A}={C}$$ |

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

1 | eqtr4d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

2 | eqtr4d.2 | $${\u22a2}{\phi}\to {C}={B}$$ | |

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

4 | 1 3 | eqtrd | $${\u22a2}{\phi}\to {A}={C}$$ |