Theorem fnrel 5672

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 5671	. 2 |- ( F Fn A -> Fun F )
2		funrel 5598	. 2 |- ( Fun F -> Rel F )
3	1, 2	syl 17	1 |- ( F Fn A -> Rel F )

Syntax hints:   -> wi 4   Rel wrel 4838   Fun wfun 5575   Fn wfn 5576

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 189  df-an 373  df-fun 5583  df-fn 5584

This theorem is referenced by:  fnbr  5676  fnresdm  5683  fn0  5693  frel  5730  fcoi2  5756  f1rel  5780  f1ocnv  5824  dffn5  5908  fnsnfv  5923  fconst5  6120  fnex  6130  fnexALT  6756  tz7.48-2  7156  zorn2lem4  8926  imasvscafn  15436  2oppchomf  15622  idssxp  28220  feqmptdf  28251  bnj66  29664  rtrclex  36218  fnresdmss  37425  dfafn5a  38656  resfnfinfin  39025