Theorem fnrel 6458

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 6457	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6375	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5541  Fun wfun 6352   Fn wfn 6353

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 210  df-an 400  df-fun 6360  df-fn 6361

This theorem is referenced by:  fnbr  6464  fnresdm  6474  fn0  6487  frel  6528  fcoi2  6572  f1rel  6596  f1ocnv  6651  dffn5  6749  feqmptdf  6760  fnsnfvOLD  6769  fconst5  6999  fnex  7011  fnexALT  7702  tz7.48-2  8156  resfnfinfin  8934  zorn2lem4  10078  imasvscafn  16996  2oppchomf  17182  fnunres1  30618  bnj66  32507  fnresdmss  42318  dfafn5a  44267