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Theorem dmexd 39940
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 7264 . 2 (𝐴𝑉 → dom 𝐴 ∈ V)
31, 2syl 17 1 (𝜑 → dom 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2140  Vcvv 3341  dom cdm 5267
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1989  ax-6 2055  ax-7 2091  ax-8 2142  ax-9 2149  ax-10 2169  ax-11 2184  ax-12 2197  ax-13 2392  ax-ext 2741  ax-sep 4934  ax-nul 4942  ax-pr 5056  ax-un 7116
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2048  df-eu 2612  df-mo 2613  df-clab 2748  df-cleq 2754  df-clel 2757  df-nfc 2892  df-rex 3057  df-rab 3060  df-v 3343  df-dif 3719  df-un 3721  df-in 3723  df-ss 3730  df-nul 4060  df-if 4232  df-sn 4323  df-pr 4325  df-op 4329  df-uni 4590  df-br 4806  df-opab 4866  df-cnv 5275  df-dm 5277  df-rn 5278
This theorem is referenced by:  sssmf  41472  mbfresmf  41473  smfpimltxr  41481  smfpimgtxr  41513  smfres  41522  smfco  41534
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