Theorem fnrel 2722

Description: A function with domain is a relation.

Assertion

Ref	Expression
fnrel	|- (F Fn A -> Rel F)

Proof of Theorem fnrel

Step	Hyp	Ref	Expression
1		fnfun 2721	. 2 |- (F Fn A -> Fun F)
2		funrel 2681	. 2 |- (Fun F -> Rel F)
3	1, 2	syl 12	1 |- (F Fn A -> Rel F)

Syntax hints:   -> wi 2  Rel wrel 2415  Fun wfun 2416   Fn wfn 2417

This theorem is referenced by:  fnresdm 2731  fn0 2739  fnex 2740  frel 2755  fcoi1 2765  fnopabfv 2858  fnsnfv 2861  cleqfv 2880  tz7.48-2 2995

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-fun 2432  df-fn 2433

metamath.org