Theorem fnrel 6641

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 6639	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
2		funrel 6556	. 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 5655  Fun wfun 6532   Fn wfn 6533

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 6540  df-fn 6541

This theorem is used by:  fnbr  6647  fnunres1  6651  fnresdm  6658  fn0  6670  frel  6715  fcoi2  6757  f1relOLD  6783  f1ocnv  6837  dffn5  6943  feqmptdf  6955  fconst5  7212  fnex  7223  fnexALT  7963  tz7.48-2  8453  zorn2lem4  10578  imasvscafn  17710  2oppchomf  17899  opprabs  34049  bnj66  35533  tfsconcatb0  44422  tfsconcat0i  44423  tfsconcat0b  44424  tfsconcat00  44425  fnresdmss  46259  dfafn5a  48306  oppfvallem  50319  funcoppc3  50331  uptposlem  50381