Users' Mathboxes Mathbox for Glauco Siliprandi < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frnd Structured version   Visualization version   GIF version

Theorem frnd 38421
Description: The range of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
frnd.1 (𝜑𝐹:𝐴𝐵)
Assertion
Ref Expression
frnd (𝜑 → ran 𝐹𝐵)

Proof of Theorem frnd
StepHypRef Expression
1 frnd.1 . 2 (𝜑𝐹:𝐴𝐵)
2 frn 5966 . 2 (𝐹:𝐴𝐵 → ran 𝐹𝐵)
31, 2syl 17 1 (𝜑 → ran 𝐹𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3540  ran crn 5039  wf 5800
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 196  df-an 385  df-f 5808
This theorem is referenced by:  preimaioomnf  39606  smfco  39687
  Copyright terms: Public domain W3C validator