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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
StepHypRef Expression
1 df-fn 4790 . 2 (F Fn A ↔ (Fun F dom F = A))
21simplbi 446 1 (F Fn A → Fun F)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1642  dom cdm 4772  Fun wfun 4775   Fn wfn 4776
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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
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