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Theorem 0domgOLD 9140
Description: Obsolete version of 0domg 9139 as of 29-Nov-2024. (Contributed by NM, 26-Oct-2003.) (Revised by Mario Carneiro, 26-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
0domgOLD (𝐴𝑉 → ∅ ≼ 𝐴)

Proof of Theorem 0domgOLD
StepHypRef Expression
1 0ss 4406 . 2 ∅ ⊆ 𝐴
2 ssdomg 9039 . 2 (𝐴𝑉 → (∅ ⊆ 𝐴 → ∅ ≼ 𝐴))
31, 2mpi 20 1 (𝐴𝑉 → ∅ ≼ 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  wss 3963  c0 4339   class class class wbr 5148  cdom 8982
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pow 5371  ax-pr 5438  ax-un 7754
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-mo 2538  df-eu 2567  df-clab 2713  df-cleq 2727  df-clel 2814  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-pw 4607  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-opab 5211  df-id 5583  df-xp 5695  df-rel 5696  df-cnv 5697  df-co 5698  df-dm 5699  df-rn 5700  df-res 5701  df-ima 5702  df-fun 6565  df-fn 6566  df-f 6567  df-f1 6568  df-fo 6569  df-f1o 6570  df-dom 8986
This theorem is referenced by: (None)
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