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Theorem fdmi 5103
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 5102 . 2  |-  ( F : A --> B  ->  dom  F  =  A )
31, 2ax-mp 7 1  |-  dom  F  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1285   dom cdm 4392   -->wf 4949
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115  df-fn 4956  df-f 4957
This theorem is referenced by:  eluzel2  8741
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