Theorem fnrel 5679

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 5678	. 2 |- ( F Fn A -> Fun F )
2		funrel 5605	. 2 |- ( Fun F -> Rel F )
3	1, 2	syl 16	1 |- ( F Fn A -> Rel F )

Syntax hints:   -> wi 4   Rel wrel 5004   Fun wfun 5582   Fn wfn 5583

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 185  df-an 371  df-fun 5590  df-fn 5591

This theorem is referenced by:  fnbr  5683  fnresdm  5690  fn0  5700  frel  5734  fcoi2  5760  f1rel  5784  f1ocnv  5828  dffn5  5913  fnsnfv  5928  fconst5  6119  fnex  6128  fnexALT  6751  tz7.48-2  7108  zorn2lem4  8880  imasvscafn  14795  2oppchomf  14983  idssxp  27239  feqmptdf  27270  fnresdmss  31248  dfafn5a  31939  resfnfinfin  32004  bnj66  33214