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Theorem fnrel 5679
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 5678 . 2  |-  ( F  Fn  A  ->  Fun  F )
2 funrel 5605 . 2  |-  ( Fun 
F  ->  Rel  F )
31, 2syl 16 1  |-  ( F  Fn  A  ->  Rel  F )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   Rel wrel 5004   Fun wfun 5582    Fn wfn 5583
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 185  df-an 371  df-fun 5590  df-fn 5591
This theorem is referenced by:  fnbr  5683  fnresdm  5690  fn0  5700  frel  5734  fcoi2  5760  f1rel  5784  f1ocnv  5828  dffn5  5913  fnsnfv  5928  fconst5  6119  fnex  6128  fnexALT  6751  tz7.48-2  7108  zorn2lem4  8880  imasvscafn  14795  2oppchomf  14983  idssxp  27239  feqmptdf  27270  fnresdmss  31248  dfafn5a  31939  resfnfinfin  32004  bnj66  33214
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