Theorem fnrel 6648

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 6646	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6562	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5680  Fun wfun 6534   Fn wfn 6535

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 6542  df-fn 6543

This theorem is referenced by:  fnbr  6654  fnunres1  6658  fnresdm  6666  fn0  6678  frel  6719  fcoi2  6763  f1rel  6787  f1ocnv  6842  dffn5  6947  feqmptdf  6959  fnsnfvOLD  6968  fconst5  7203  fnex  7215  fnexALT  7933  tz7.48-2  8438  resfnfinfin  9328  zorn2lem4  10490  imasvscafn  17479  2oppchomf  17666  opprabs  32584  bnj66  33859  tfsconcatb0  42079  tfsconcat0i  42080  tfsconcat0b  42081  tfsconcat00  42082  fnresdmss  43849  dfafn5a  45854