ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  funforn GIF version

Theorem funforn 5141
Description: A function maps its domain onto its range. (Contributed by NM, 23-Jul-2004.)
Assertion
Ref Expression
funforn (Fun 𝐴𝐴:dom 𝐴onto→ran 𝐴)

Proof of Theorem funforn
StepHypRef Expression
1 funfn 4959 . 2 (Fun 𝐴𝐴 Fn dom 𝐴)
2 dffn4 5140 . 2 (𝐴 Fn dom 𝐴𝐴:dom 𝐴onto→ran 𝐴)
31, 2bitri 177 1 (Fun 𝐴𝐴:dom 𝐴onto→ran 𝐴)
Colors of variables: wff set class
Syntax hints:  wb 102  dom cdm 4373  ran crn 4374  Fun wfun 4924   Fn wfn 4925  ontowfo 4928
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-gen 1354  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-fn 4933  df-fo 4936
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator