ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  funfnd Unicode version

Theorem funfnd 5158
Description: A function is a function over its domain. (Contributed by Glauco Siliprandi, 23-Oct-2021.)
Hypothesis
Ref Expression
funfnd.1  |-  ( ph  ->  Fun  A )
Assertion
Ref Expression
funfnd  |-  ( ph  ->  A  Fn  dom  A
)

Proof of Theorem funfnd
StepHypRef Expression
1 funfnd.1 . 2  |-  ( ph  ->  Fun  A )
2 funfn 5157 . 2  |-  ( Fun 
A  <->  A  Fn  dom  A )
31, 2sylib 121 1  |-  ( ph  ->  A  Fn  dom  A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   dom cdm 4543   Fun wfun 5121    Fn wfn 5122
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1426  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-cleq 2133  df-fn 5130
This theorem is referenced by:  ennnfonelemf1  11958  dvfgg  12856
  Copyright terms: Public domain W3C validator