Theorem fnrel 6637

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 6635	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6553	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 18	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5666  Fun wfun 6530   Fn wfn 6531

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 6538  df-fn 6539

This theorem is referenced by:  fnbr  6643  fnunres1  6647  fnresdm  6654  fn0  6666  frel  6711  fcoi2  6753  f1relOLD  6779  f1ocnv  6833  dffn5  6939  feqmptdf  6951  fconst5  7204  fnex  7215  fnexALT  7947  tz7.48-2  8428  zorn2lem4  10482  imasvscafn  17590  2oppchomf  17779  opprabs  33730  bnj66  35214  tfsconcatb0  44041  tfsconcat0i  44042  tfsconcat0b  44043  tfsconcat00  44044  fnresdmss  45856  dfafn5a  47864  oppfvallem  49880  funcoppc3  49892  uptposlem  49942