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Theorem fdmd 38894
Description: The domain of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
fdmd.1 (𝜑𝐹:𝐴𝐵)
Assertion
Ref Expression
fdmd (𝜑 → dom 𝐹 = 𝐴)

Proof of Theorem fdmd
StepHypRef Expression
1 fdmd.1 . 2 (𝜑𝐹:𝐴𝐵)
2 fdm 6008 . 2 (𝐹:𝐴𝐵 → dom 𝐹 = 𝐴)
31, 2syl 17 1 (𝜑 → dom 𝐹 = 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1480  dom cdm 5074  wf 5843
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 386  df-fn 5850  df-f 5851
This theorem is referenced by:  limsuppnfdlem  39337  limsupvaluz  39344  issmfd  40251  issmfdf  40253  cnfsmf  40256  issmfled  40273  smfmbfcex  40275  issmfgtd  40276  smfsuplem1  40324
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