Theorem fnrel 5683

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

Step	Hyp	Ref	Expression
1		fnfun 5682	. 2 |- ( F Fn A -> Fun F )
2		funrel 5609	. 2 |- ( Fun F -> Rel F )
3	1, 2	syl 17	1 |- ( F Fn A -> Rel F )

Syntax hints:   -> wi 4   Rel wrel 4850   Fun wfun 5586   Fn wfn 5587

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 188  df-an 372  df-fun 5594  df-fn 5595

This theorem is referenced by:  fnbr  5687  fnresdm  5694  fn0  5704  frel  5740  fcoi2  5766  f1rel  5790  f1ocnv  5834  dffn5  5917  fnsnfv  5932  fconst5  6128  fnex  6138  fnexALT  6764  tz7.48-2  7158  zorn2lem4  8918  imasvscafn  15395  2oppchomf  15581  idssxp  28108  feqmptdf  28139  bnj66  29500  fnresdmss  37101  dfafn5a  38109  resfnfinfin  38444