Theorem fnrel 5268

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 5267	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 5187	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 4591  Fun wfun 5164   Fn wfn 5165

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105

This theorem depends on definitions:  df-bi 116  df-fun 5172  df-fn 5173

This theorem is referenced by:  fnbr  5272  fnresdm  5279  fn0  5289  frel  5324  fcoi2  5351  f1rel  5379  f1ocnv  5427  dffn5im  5514  fnex  5689  fnexALT  6061  istps  12441  topontopn  12446  cldrcl  12513  neiss2  12553