Theorem fnrel 5106

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 5105	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 5027	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 4441  Fun wfun 5004   Fn wfn 5005

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 5012  df-fn 5013

This theorem is referenced by:  fnbr  5110  fnresdm  5117  fn0  5127  frel  5159  fcoi2  5186  f1rel  5214  f1ocnv  5260  dffn5im  5344  fnex  5511  fnexALT  5876