Theorem fnrel 5216

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 5215	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 5135	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 14	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 4539  Fun wfun 5112   Fn wfn 5113

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 5120  df-fn 5121

This theorem is referenced by:  fnbr  5220  fnresdm  5227  fn0  5237  frel  5272  fcoi2  5299  f1rel  5327  f1ocnv  5373  dffn5im  5460  fnex  5635  fnexALT  6004  istps  12188  topontopn  12193  cldrcl  12260  neiss2  12300