**Description:** Deduction form of frn . The range of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021)

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

Hypothesis | frnd.1 | $${\u22a2}{\phi}\to {F}:{A}\u27f6{B}$$ | |

Assertion | frnd | $${\u22a2}{\phi}\to \mathrm{ran}{F}\subseteq {B}$$ |

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

1 | frnd.1 | $${\u22a2}{\phi}\to {F}:{A}\u27f6{B}$$ | |

2 | frn | $${\u22a2}{F}:{A}\u27f6{B}\to \mathrm{ran}{F}\subseteq {B}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to \mathrm{ran}{F}\subseteq {B}$$ |