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Theorem dmexd 38914
 Description: The domain of a set is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
dmexd.1 (𝜑𝐴𝑉)
Assertion
Ref Expression
dmexd (𝜑 → dom 𝐴 ∈ V)

Proof of Theorem dmexd
StepHypRef Expression
1 dmexd.1 . 2 (𝜑𝐴𝑉)
2 dmexg 7047 . 2 (𝐴𝑉 → dom 𝐴 ∈ V)
31, 2syl 17 1 (𝜑 → dom 𝐴 ∈ V)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1987  Vcvv 3186  dom cdm 5076 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-8 1989  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4743  ax-nul 4751  ax-pr 4869  ax-un 6905 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-mo 2474  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rex 2913  df-rab 2916  df-v 3188  df-dif 3559  df-un 3561  df-in 3563  df-ss 3570  df-nul 3894  df-if 4061  df-sn 4151  df-pr 4153  df-op 4157  df-uni 4405  df-br 4616  df-opab 4676  df-cnv 5084  df-dm 5086  df-rn 5087 This theorem is referenced by:  sssmf  40270  mbfresmf  40271  smfpimltxr  40279  smfpimgtxr  40311  smfres  40320  smfco  40332
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