ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  f1fn Unicode version

Theorem f1fn 5419
Description: A one-to-one mapping is a function on its domain. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1fn  |-  ( F : A -1-1-> B  ->  F  Fn  A )

Proof of Theorem f1fn
StepHypRef Expression
1 f1f 5417 . 2  |-  ( F : A -1-1-> B  ->  F : A --> B )
2 ffn 5361 . 2  |-  ( F : A --> B  ->  F  Fn  A )
31, 2syl 14 1  |-  ( F : A -1-1-> B  ->  F  Fn  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    Fn wfn 5207   -->wf 5208   -1-1->wf1 5209
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106
This theorem depends on definitions:  df-bi 117  df-f 5216  df-f1 5217
This theorem is referenced by:  f1fun  5420  f1rel  5421  f1dm  5422  f1ssr  5424  f1f1orn  5468  f1elima  5768  f1eqcocnv  5786  f1oiso  5821  phplem4dom  6856  f1finf1o  6940  updjudhcoinlf  7073  updjudhcoinrg  7074  updjud  7075  fihashf1rn  10752
  Copyright terms: Public domain W3C validator