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Theorem fdmi 5280
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 5278 . 2 (𝐹:𝐴𝐵 → dom 𝐹 = 𝐴)
31, 2ax-mp 5 1 dom 𝐹 = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1331  dom cdm 4539  wf 5119
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116  df-fn 5126  df-f 5127
This theorem is referenced by:  suplocexprlemdisj  7535  suplocexprlemub  7538  eluzel2  9338  inftonninf  10221  qtopbasss  12700  retopbas  12702  tgqioo  12726  dvexp  12854  efcn  12867  pilem3  12877
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