Theorem fnrel 5903

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 5902	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 5821	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5043  Fun wfun 5798   Fn wfn 5799

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 196  df-an 385  df-fun 5806  df-fn 5807

This theorem is referenced by:  fnbr  5907  fnresdm  5914  fn0  5924  frel  5963  fcoi2  5992  f1rel  6017  f1ocnv  6062  dffn5  6151  feqmptdf  6161  fnsnfv  6168  fconst5  6376  fnex  6386  fnexALT  7025  tz7.48-2  7424  zorn2lem4  9204  imasvscafn  16020  2oppchomf  16207  idssxp  28811  bnj66  30184  rtrclex  36943  fnresdmss  38342  dfafn5a  39889  resfnfinfin  40339