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Theorem fdmd 39938
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 6191 . 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 1631  dom cdm 5249  wf 6027
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 383  df-fn 6034  df-f 6035
This theorem is referenced by:  limsuppnfdlem  40451  limsupvaluz  40458  climxrrelem  40499  climxrre  40500  liminfvalxr  40533  xlimmnfvlem2  40577  xlimpnfvlem2  40581  issmfd  41464  issmfdf  41466  cnfsmf  41469  issmfled  41486  smfmbfcex  41488  issmfgtd  41489  smfsuplem1  41537
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