Theorem fnfun 5182

Description: A function with domain is a function. (Contributed by set.mm contributors, 1-Aug-1994.)

Assertion

Ref	Expression
fnfun	⊢ (F Fn A → Fun F)

Proof of Theorem fnfun

Step	Hyp	Ref	Expression
1		df-fn 4791	. 2 ⊢ (F Fn A ↔ (Fun F ∧ dom F = A))
2	1	simplbi 446	1 ⊢ (F Fn A → Fun F)

Syntax hints:   → wi 4   = wceq 1642  dom cdm 4773  Fun wfun 4776   Fn wfn 4777

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 177  df-an 360  df-fn 4791

This theorem is referenced by:  funfni  5184  fnco  5192  fnssresb  5196  ffun  5226  f1fun  5261  f1ofun  5290  fvelimab  5371  fvun1  5380  elpreima  5408  respreima  5411  fconst3  5458  enprmaplem3  6079  frecsuc  6323