Theorem fnrel 6681

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 6679	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6595	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5705  Fun wfun 6567   Fn wfn 6568

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 207  df-an 396  df-fun 6575  df-fn 6576

This theorem is referenced by:  fnbr  6687  fnunres1  6691  fnresdm  6699  fn0  6711  frel  6752  fcoi2  6796  f1rel  6820  f1ocnv  6874  dffn5  6980  feqmptdf  6992  fconst5  7243  fnex  7254  fnexALT  7991  tz7.48-2  8498  resfnfinfin  9405  zorn2lem4  10568  imasvscafn  17597  2oppchomf  17784  opprabs  33475  bnj66  34836  tfsconcatb0  43306  tfsconcat0i  43307  tfsconcat0b  43308  tfsconcat00  43309  fnresdmss  45075  dfafn5a  47075