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

Proof of Theorem funfnd
StepHypRef Expression
1 funfnd.1 . 2 (𝜑 → Fun 𝐴)
2 funfn 5157 . 2 (Fun 𝐴𝐴 Fn dom 𝐴)
31, 2sylib 121 1 (𝜑𝐴 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
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