Theorem fnrel 6448

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 6447	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6366	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5554  Fun wfun 6343   Fn wfn 6344

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 6351  df-fn 6352

This theorem is referenced by:  fnbr  6453  fnresdm  6460  fn0  6473  frel  6513  fcoi2  6547  f1rel  6572  f1ocnv  6621  dffn5  6718  feqmptdf  6729  fnsnfv  6737  fconst5  6962  fnex  6974  fnexALT  7646  tz7.48-2  8072  resfnfinfin  8798  zorn2lem4  9915  imasvscafn  16804  2oppchomf  16988  fnunres1  30350  bnj66  32127  fnimasnd  39114  fnresdmss  41417  dfafn5a  43353