Theorem fnrel 6657

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 6655	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6571	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5683  Fun wfun 6543   Fn wfn 6544

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 395  df-fun 6551  df-fn 6552

This theorem is referenced by:  fnbr  6663  fnunres1  6667  fnresdm  6675  fn0  6687  frel  6728  fcoi2  6772  f1rel  6796  f1ocnv  6850  dffn5  6956  feqmptdf  6968  fnsnfvOLD  6977  fconst5  7218  fnex  7229  fnexALT  7955  tz7.48-2  8463  resfnfinfin  9358  zorn2lem4  10524  imasvscafn  17522  2oppchomf  17709  opprabs  33294  bnj66  34622  tfsconcatb0  42915  tfsconcat0i  42916  tfsconcat0b  42917  tfsconcat00  42918  fnresdmss  44680  dfafn5a  46678