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

Theorem fnrel 6605
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 6603 . 2 (𝐹 Fn 𝐴 → Fun 𝐹)
2 funrel 6519 . 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 5639  Fun wfun 6491   Fn wfn 6492
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 206  df-an 398  df-fun 6499  df-fn 6500
This theorem is referenced by:  fnbr  6611  fnresdm  6621  fn0  6633  frel  6674  fcoi2  6718  f1rel  6742  f1ocnv  6797  dffn5  6902  feqmptdf  6913  fnsnfvOLD  6922  fconst5  7156  fnex  7168  fnexALT  7884  tz7.48-2  8389  resfnfinfin  9277  zorn2lem4  10436  imasvscafn  17420  2oppchomf  17607  fnunres1  31527  bnj66  33475  fnresdmss  43392  dfafn5a  45399
  Copyright terms: Public domain W3C validator