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Theorem fdmi 5372
Description: The domain of a mapping. (Contributed by NM, 28-Jul-2008.)
Hypothesis
Ref Expression
fdmi.1  |-  F : A
--> B
Assertion
Ref Expression
fdmi  |-  dom  F  =  A

Proof of Theorem fdmi
StepHypRef Expression
1 fdmi.1 . 2  |-  F : A
--> B
2 fdm 5370 . 2  |-  ( F : A --> B  ->  dom  F  =  A )
31, 2ax-mp 5 1  |-  dom  F  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1353   dom cdm 4625   -->wf 5211
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107
This theorem depends on definitions:  df-bi 117  df-fn 5218  df-f 5219
This theorem is referenced by:  suplocexprlemdisj  7716  suplocexprlemub  7719  eluzel2  9529  inftonninf  10436  qtopbasss  13892  retopbas  13894  tgqioo  13918  dvexp  14046  efcn  14060  pilem3  14075
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