Theorem fnrel 6627

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 6625	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6542	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 18	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5657  Fun wfun 6519   Fn wfn 6520

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 401  df-fun 6527  df-fn 6528

This theorem is referenced by:  fnbr  6633  fnunres1  6637  fnresdm  6644  fn0  6656  frel  6701  fcoi2  6743  f1relOLD  6769  f1ocnv  6823  dffn5  6929  feqmptdf  6941  fconst5  7194  fnex  7205  fnexALT  7936  tz7.48-2  8417  zorn2lem4  10471  imasvscafn  17581  2oppchomf  17770  opprabs  33681  bnj66  35165  tfsconcatb0  43933  tfsconcat0i  43934  tfsconcat0b  43935  tfsconcat00  43936  fnresdmss  45744  dfafn5a  47752  oppfvallem  49764  funcoppc3  49776  uptposlem  49826