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Theorem fdmi 5168
Description: The domain of a mapping. (Contributed by NM, 28-Jul-2008.)
Hypothesis
Ref Expression
fdmi.1 𝐹:𝐴𝐵
Assertion
Ref Expression
fdmi dom 𝐹 = 𝐴

Proof of Theorem fdmi
StepHypRef Expression
1 fdmi.1 . 2 𝐹:𝐴𝐵
2 fdm 5166 . 2 (𝐹:𝐴𝐵 → dom 𝐹 = 𝐴)
31, 2ax-mp 7 1 dom 𝐹 = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1289  dom cdm 4438  wf 5011
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 5018  df-f 5019
This theorem is referenced by:  eluzel2  9024  inftonninf  9847
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