Theorem fnfun 5181

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 4790	. 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 4772  Fun wfun 4775   Fn wfn 4776

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 4790

This theorem is referenced by:  funfni  5183  fnco  5191  fnssresb  5195  ffun  5225  f1fun  5260  f1ofun  5289  fvelimab  5370  fvun1  5379  elpreima  5407  respreima  5410  fconst3  5457  enprmaplem3  6078  frecsuc  6322