Theorem fnrel 6670

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 6668	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6583	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5690  Fun wfun 6555   Fn wfn 6556

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 207  df-an 396  df-fun 6563  df-fn 6564

This theorem is referenced by:  fnbr  6676  fnunres1  6680  fnresdm  6687  fn0  6699  frel  6741  fcoi2  6783  f1rel  6807  f1ocnv  6860  dffn5  6967  feqmptdf  6979  fconst5  7226  fnex  7237  fnexALT  7975  tz7.48-2  8482  resfnfinfin  9377  zorn2lem4  10539  imasvscafn  17582  2oppchomf  17767  opprabs  33510  bnj66  34874  tfsconcatb0  43357  tfsconcat0i  43358  tfsconcat0b  43359  tfsconcat00  43360  fnresdmss  45173  dfafn5a  47172