Theorem fnrel 6642

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 6640	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6556	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5672  Fun wfun 6528   Fn wfn 6529

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 6536  df-fn 6537

This theorem is referenced by:  fnbr  6648  fnunres1  6652  fnresdm  6660  fn0  6672  frel  6713  fcoi2  6757  f1rel  6781  f1ocnv  6836  dffn5  6941  feqmptdf  6953  fnsnfvOLD  6962  fconst5  7200  fnex  7211  fnexALT  7931  tz7.48-2  8438  resfnfinfin  9329  zorn2lem4  10491  imasvscafn  17488  2oppchomf  17675  opprabs  33091  bnj66  34389  tfsconcatb0  42643  tfsconcat0i  42644  tfsconcat0b  42645  tfsconcat00  42646  fnresdmss  44412  dfafn5a  46413