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Theorem fnrel 5672
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 5671 . 2  |-  ( F  Fn  A  ->  Fun  F )
2 funrel 5598 . 2  |-  ( Fun 
F  ->  Rel  F )
31, 2syl 17 1  |-  ( F  Fn  A  ->  Rel  F )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   Rel wrel 4838   Fun wfun 5575    Fn wfn 5576
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 189  df-an 373  df-fun 5583  df-fn 5584
This theorem is referenced by:  fnbr  5676  fnresdm  5683  fn0  5693  frel  5730  fcoi2  5756  f1rel  5780  f1ocnv  5824  dffn5  5908  fnsnfv  5923  fconst5  6120  fnex  6130  fnexALT  6756  tz7.48-2  7156  zorn2lem4  8926  imasvscafn  15436  2oppchomf  15622  idssxp  28220  feqmptdf  28251  bnj66  29664  rtrclex  36218  fnresdmss  37425  dfafn5a  38656  resfnfinfin  39025
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