MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  fnrel Unicode version

Theorem fnrel 5483
Description: A function with domain is a relation. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
fnrel  |-  ( F  Fn  A  ->  Rel  F )

Proof of Theorem fnrel
StepHypRef Expression
1 fnfun 5482 . 2  |-  ( F  Fn  A  ->  Fun  F )
2 funrel 5411 . 2  |-  ( Fun 
F  ->  Rel  F )
31, 2syl 16 1  |-  ( F  Fn  A  ->  Rel  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Rel wrel 4823   Fun wfun 5388    Fn wfn 5389
This theorem is referenced by:  fnbr  5487  fnresdm  5494  fn0  5504  frel  5534  fcoi2  5558  f1rel  5582  f1ocnv  5627  dffn5  5711  fnsnfv  5725  fconst5  5888  fnex  5900  fnexALT  5901  tz7.48-2  6635  zorn2lem4  8312  imasvscafn  13689  2oppchomf  13877  feqmptdf  23917  dfafn5a  27693  bnj66  28569
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361  df-fun 5396  df-fn 5397
  Copyright terms: Public domain W3C validator