**Description:** Equality deduction for unordered pairs. (Contributed by NM, 19-Oct-2012)

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

Hypothesis | preq1d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

Assertion | preq2d | $${\u22a2}{\phi}\to \left\{{C},{A}\right\}=\left\{{C},{B}\right\}$$ |

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

1 | preq1d.1 | $${\u22a2}{\phi}\to {A}={B}$$ | |

2 | preq2 | $${\u22a2}{A}={B}\to \left\{{C},{A}\right\}=\left\{{C},{B}\right\}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to \left\{{C},{A}\right\}=\left\{{C},{B}\right\}$$ |