Theorem fnrel 5229

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 5228	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 5148	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 4552  Fun wfun 5125   Fn wfn 5126

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 5133  df-fn 5134

This theorem is referenced by:  fnbr  5233  fnresdm  5240  fn0  5250  frel  5285  fcoi2  5312  f1rel  5340  f1ocnv  5388  dffn5im  5475  fnex  5650  fnexALT  6019  istps  12238  topontopn  12243  cldrcl  12310  neiss2  12350