**Description:** A deduction from three chained equalities. (Contributed by NM, 21-Sep-1995)

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

Hypotheses | 3eqtr4d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

3eqtr4d.2 | $${\u22a2}{\phi}\to {C}={A}$$ | ||

3eqtr4d.3 | $${\u22a2}{\phi}\to {D}={B}$$ | ||

Assertion | 3eqtr4rd | $${\u22a2}{\phi}\to {D}={C}$$ |

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

1 | 3eqtr4d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

2 | 3eqtr4d.2 | $${\u22a2}{\phi}\to {C}={A}$$ | |

3 | 3eqtr4d.3 | $${\u22a2}{\phi}\to {D}={B}$$ | |

4 | 3 1 | eqtr4d | $${\u22a2}{\phi}\to {D}={A}$$ |

5 | 4 2 | eqtr4d | $${\u22a2}{\phi}\to {D}={C}$$ |