Theorem fnrel 5017

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 5016	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 4939	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 4368  Fun wfun 4916   Fn wfn 4917

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-fun 4924  df-fn 4925

This theorem is referenced by:  fnbr  5021  fnresdm  5028  fn0  5038  frel  5069  fcoi2  5091  f1rel  5115  f1ocnv  5159  dffn5im  5240  fnex  5404  fnexALT  5760