**Description:** A deduction from three chained equalities. (Contributed by NM, 4-Aug-2006)

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

Hypotheses | 3eqtr2d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

3eqtr2d.2 | $${\u22a2}{\phi}\to {C}={B}$$ | ||

3eqtr2d.3 | $${\u22a2}{\phi}\to {C}={D}$$ | ||

Assertion | 3eqtr2d | $${\u22a2}{\phi}\to {A}={D}$$ |

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

1 | 3eqtr2d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

2 | 3eqtr2d.2 | $${\u22a2}{\phi}\to {C}={B}$$ | |

3 | 3eqtr2d.3 | $${\u22a2}{\phi}\to {C}={D}$$ | |

4 | 1 2 | eqtr4d | $${\u22a2}{\phi}\to {A}={C}$$ |

5 | 4 3 | eqtrd | $${\u22a2}{\phi}\to {A}={D}$$ |