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Theorem funfnd 6061
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 6060 . 2 (Fun 𝐴𝐴 Fn dom 𝐴)
31, 2sylib 208 1 (𝜑𝐴 Fn dom 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  dom cdm 5250  Fun wfun 6024   Fn wfn 6025
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853  df-cleq 2764  df-fn 6033
This theorem is referenced by:  wfrlem4  7574  uhgrvtxedgiedgb  26252  ushgredgedgloop  26345  upgrres  26421  umgrres  26422  funimaeq  39976  limsupresxr  40513  liminfresxr  40514
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