Theorem fnrel 6519

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 6517	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6435	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5585  Fun wfun 6412   Fn wfn 6413

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 396  df-fun 6420  df-fn 6421

This theorem is referenced by:  fnbr  6525  fnresdm  6535  fn0  6548  frel  6589  fcoi2  6633  f1rel  6657  f1ocnv  6712  dffn5  6810  feqmptdf  6821  fnsnfvOLD  6830  fconst5  7063  fnex  7075  fnexALT  7767  tz7.48-2  8243  resfnfinfin  9029  zorn2lem4  10186  imasvscafn  17165  2oppchomf  17352  fnunres1  30846  bnj66  32740  fnresdmss  42593  dfafn5a  44539