ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  f1dm Unicode version

Theorem f1dm 5121
Description: The domain of a one-to-one mapping. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1dm  |-  ( F : A -1-1-> B  ->  dom  F  =  A )

Proof of Theorem f1dm
StepHypRef Expression
1 f1fn 5118 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fndm 5023 . 2  |-  ( F  Fn  A  ->  dom  F  =  A )
31, 2syl 14 1  |-  ( F : A -1-1-> B  ->  dom  F  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285   dom cdm 4365    Fn wfn 4921   -1-1->wf1 4923
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115  df-fn 4929  df-f 4930  df-f1 4931
This theorem is referenced by:  fun11iun  5172  tposf12  5912  f1dmvrnfibi  6442  f1vrnfibi  6443
  Copyright terms: Public domain W3C validator