Theorem fnrel 5989

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 5988	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 5905	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5119  Fun wfun 5882   Fn wfn 5883

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 197  df-an 386  df-fun 5890  df-fn 5891

This theorem is referenced by:  fnbr  5993  fnresdm  6000  idssxp  6009  fn0  6011  frel  6050  fcoi2  6079  f1rel  6104  f1ocnv  6149  dffn5  6241  feqmptdf  6251  fnsnfv  6258  fconst5  6471  fnex  6481  fnexALT  7132  tz7.48-2  7537  resfnfinfin  8246  zorn2lem4  9321  imasvscafn  16197  2oppchomf  16384  fnunres1  29417  bnj66  30930  rtrclex  37924  fnresdmss  39348  dfafn5a  41240