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

Theorem fnrel 5949
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 5948 . 2 (𝐹 Fn 𝐴 → Fun 𝐹)
2 funrel 5866 . 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 5081  Fun wfun 5843   Fn wfn 5844
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 197  df-an 386  df-fun 5851  df-fn 5852
This theorem is referenced by:  fnbr  5953  fnresdm  5960  fn0  5970  frel  6009  fcoi2  6038  f1rel  6063  f1ocnv  6108  dffn5  6200  feqmptdf  6210  fnsnfv  6217  fconst5  6428  fnex  6438  fnexALT  7082  tz7.48-2  7485  resfnfinfin  8193  zorn2lem4  9268  imasvscafn  16121  2oppchomf  16308  idssxp  29285  bnj66  30659  rtrclex  37426  fnresdmss  38840  dfafn5a  40560
  Copyright terms: Public domain W3C validator