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

Theorem funforn 5056
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 4874 . 2 (Fun AA Fn dom A)
2 dffn4 5055 . 2 (A Fn dom AA:dom Aonto→ran A)
31, 2bitri 173 1 (Fun AA:dom Aonto→ran A)
Colors of variables: wff set class
Syntax hints:  wb 98  dom cdm 4288  ran crn 4289  Fun wfun 4839   Fn wfn 4840  ontowfo 4843
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1335  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-fn 4848  df-fo 4851
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator