Theorem fnrel 6457

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 6456	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6375	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5563  Fun wfun 6352   Fn wfn 6353

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 209  df-an 399  df-fun 6360  df-fn 6361

This theorem is referenced by:  fnbr  6462  fnresdm  6469  fn0  6482  frel  6522  fcoi2  6556  f1rel  6581  f1ocnv  6630  dffn5  6727  feqmptdf  6738  fnsnfv  6746  fconst5  6971  fnex  6983  fnexALT  7655  tz7.48-2  8081  resfnfinfin  8807  zorn2lem4  9924  imasvscafn  16813  2oppchomf  16997  fnunres1  30359  bnj66  32136  fnimasnd  39127  fnresdmss  41430  dfafn5a  43366