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Theorem fnrel 6284
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 6283 . 2 (𝐹 Fn 𝐴 → Fun 𝐹)
2 funrel 6202 . 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 5408  Fun wfun 6179   Fn wfn 6180
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 199  df-an 388  df-fun 6187  df-fn 6188
This theorem is referenced by:  fnbr  6289  fnresdm  6296  fn0  6306  frel  6346  fcoi2  6379  f1rel  6404  f1ocnv  6453  dffn5  6551  feqmptdf  6562  fnsnfv  6569  fconst5  6793  fnex  6804  fnexALT  7462  tz7.48-2  7879  resfnfinfin  8597  zorn2lem4  9717  imasvscafn  16664  2oppchomf  16864  fnunres1  30137  bnj66  31811  fnimasnd  38604  rtrclex  39378  fnresdmss  40883  dfafn5a  42799
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