Theorem fnrel 6531

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 6529	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6447	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5593  Fun wfun 6424   Fn wfn 6425

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 206  df-an 396  df-fun 6432  df-fn 6433

This theorem is referenced by:  fnbr  6537  fnresdm  6547  fn0  6560  frel  6601  fcoi2  6645  f1rel  6669  f1ocnv  6724  dffn5  6822  feqmptdf  6833  fnsnfvOLD  6842  fconst5  7075  fnex  7087  fnexALT  7780  tz7.48-2  8257  resfnfinfin  9060  zorn2lem4  10239  imasvscafn  17229  2oppchomf  17416  fnunres1  30924  bnj66  32819  fnresdmss  42657  dfafn5a  44603