Theorem fnrel 6284

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 6283	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6202	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5408  Fun wfun 6179   Fn wfn 6180

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 199  df-an 388  df-fun 6187  df-fn 6188

This theorem is referenced by:  fnbr  6289  fnresdm  6296  fn0  6306  frel  6346  fcoi2  6379  f1rel  6404  f1ocnv  6453  dffn5  6551  feqmptdf  6562  fnsnfv  6569  fconst5  6793  fnex  6804  fnexALT  7462  tz7.48-2  7879  resfnfinfin  8597  zorn2lem4  9717  imasvscafn  16664  2oppchomf  16864  fnunres1  30137  bnj66  31811  fnimasnd  38604  rtrclex  39378  fnresdmss  40883  dfafn5a  42799