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Theorem 0domgOLD 9132
Description: Obsolete version of 0domg 9131 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 4400 . 2 ∅ ⊆ 𝐴
2 ssdomg 9027 . 2 (𝐴𝑉 → (∅ ⊆ 𝐴 → ∅ ≼ 𝐴))
31, 2mpi 20 1 (𝐴𝑉 → ∅ ≼ 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  wss 3949  c0 4326   class class class wbr 5152  cdom 8968
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-12 2166  ax-ext 2699  ax-sep 5303  ax-nul 5310  ax-pow 5369  ax-pr 5433  ax-un 7746
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2529  df-eu 2558  df-clab 2706  df-cleq 2720  df-clel 2806  df-ral 3059  df-rex 3068  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-pw 4608  df-sn 4633  df-pr 4635  df-op 4639  df-uni 4913  df-br 5153  df-opab 5215  df-id 5580  df-xp 5688  df-rel 5689  df-cnv 5690  df-co 5691  df-dm 5692  df-rn 5693  df-res 5694  df-ima 5695  df-fun 6555  df-fn 6556  df-f 6557  df-f1 6558  df-fo 6559  df-f1o 6560  df-dom 8972
This theorem is referenced by: (None)
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