Theorem fnrel 5221

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 5220	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 5140	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 4544  Fun wfun 5117   Fn wfn 5118

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 5125  df-fn 5126

This theorem is referenced by:  fnbr  5225  fnresdm  5232  fn0  5242  frel  5277  fcoi2  5304  f1rel  5332  f1ocnv  5380  dffn5im  5467  fnex  5642  fnexALT  6011  istps  12199  topontopn  12204  cldrcl  12271  neiss2  12311