**Description:** Equality deduction for restrictions. (Contributed by Paul Chapman, 22-Jun-2011)

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

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

Assertion | reseq2d | $${\u22a2}{\phi}\to {{C}\upharpoonright}_{{A}}={{C}\upharpoonright}_{{B}}$$ |

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

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

2 | reseq2 | $${\u22a2}{A}={B}\to {{C}\upharpoonright}_{{A}}={{C}\upharpoonright}_{{B}}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to {{C}\upharpoonright}_{{A}}={{C}\upharpoonright}_{{B}}$$ |