Theorem fnrel 6638

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 6636	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6554	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 18	1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹)

This proof depends on syntax axioms:   → wi 4  Rel wrel 5664  Fun wfun 6531   Fn wfn 6532

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-fun 6539  df-fn 6540

This theorem is used by:  fnbr  6644  fnunres1  6648  fnresdm  6655  fn0  6667  frel  6712  fcoi2  6754  f1relOLD  6780  f1ocnv  6834  dffn5  6940  feqmptdf  6952  fconst5  7208  fnex  7219  fnexALT  7951  tz7.48-2  8434  zorn2lem4  10504  imasvscafn  17627  2oppchomf  17816  opprabs  33886  bnj66  35371  tfsconcatb0  44187  tfsconcat0i  44188  tfsconcat0b  44189  tfsconcat00  44190  fnresdmss  46002  dfafn5a  48050  oppfvallem  50063  funcoppc3  50075  uptposlem  50125