**Description:** Substitution of equality into both sides of a binary relation.
(Contributed by NM, 16-Jan-1997)

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

Hypotheses | 3brtr3g.1 | $${\u22a2}{\phi}\to {A}{R}{B}$$ | |

3brtr3g.2 | $${\u22a2}{A}={C}$$ | ||

3brtr3g.3 | $${\u22a2}{B}={D}$$ | ||

Assertion | 3brtr3g | $${\u22a2}{\phi}\to {C}{R}{D}$$ |

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

1 | 3brtr3g.1 | $${\u22a2}{\phi}\to {A}{R}{B}$$ | |

2 | 3brtr3g.2 | $${\u22a2}{A}={C}$$ | |

3 | 3brtr3g.3 | $${\u22a2}{B}={D}$$ | |

4 | 2 3 | breq12i | $${\u22a2}{A}{R}{B}\leftrightarrow {C}{R}{D}$$ |

5 | 1 4 | sylib | $${\u22a2}{\phi}\to {C}{R}{D}$$ |