Theorem fnrel 6535

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 6533	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6451	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5594  Fun wfun 6427   Fn wfn 6428

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 397  df-fun 6435  df-fn 6436

This theorem is referenced by:  fnbr  6541  fnresdm  6551  fn0  6564  frel  6605  fcoi2  6649  f1rel  6673  f1ocnv  6728  dffn5  6828  feqmptdf  6839  fnsnfvOLD  6848  fconst5  7081  fnex  7093  fnexALT  7793  tz7.48-2  8273  resfnfinfin  9099  zorn2lem4  10255  imasvscafn  17248  2oppchomf  17435  fnunres1  30945  bnj66  32840  fnresdmss  42704  dfafn5a  44652