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 6584	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5693  Fun wfun 6556   Fn wfn 6557

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 6564  df-fn 6565

This theorem is referenced by:  fnbr  6676  fnunres1  6680  fnresdm  6687  fn0  6699  frel  6741  fcoi2  6783  f1rel  6807  f1ocnv  6860  dffn5  6966  feqmptdf  6978  fconst5  7225  fnex  7236  fnexALT  7973  tz7.48-2  8480  resfnfinfin  9374  zorn2lem4  10536  imasvscafn  17583  2oppchomf  17770  opprabs  33489  bnj66  34852  tfsconcatb0  43333  tfsconcat0i  43334  tfsconcat0b  43335  tfsconcat00  43336  fnresdmss  45110  dfafn5a  47109