Theorem fnrel 6656

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 6654	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6570	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5683  Fun wfun 6542   Fn wfn 6543

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396  df-fun 6550  df-fn 6551

This theorem is referenced by:  fnbr  6662  fnunres1  6666  fnresdm  6674  fn0  6686  frel  6727  fcoi2  6772  f1rel  6796  f1ocnv  6851  dffn5  6957  feqmptdf  6969  fnsnfvOLD  6978  fconst5  7218  fnex  7229  fnexALT  7954  tz7.48-2  8462  resfnfinfin  9356  zorn2lem4  10522  imasvscafn  17518  2oppchomf  17705  opprabs  33193  bnj66  34491  tfsconcatb0  42773  tfsconcat0i  42774  tfsconcat0b  42775  tfsconcat00  42776  fnresdmss  44541  dfafn5a  46540