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Theorem bnj923 32252
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj923.1 𝐷 = (ω ∖ {∅})
Assertion
Ref Expression
bnj923 (𝑛𝐷𝑛 ∈ ω)

Proof of Theorem bnj923
StepHypRef Expression
1 eldifi 4028 . 2 (𝑛 ∈ (ω ∖ {∅}) → 𝑛 ∈ ω)
2 bnj923.1 . 2 𝐷 = (ω ∖ {∅})
31, 2eleq2s 2869 1 (𝑛𝐷𝑛 ∈ ω)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1539   ∈ wcel 2112   ∖ cdif 3851  ∅c0 4221  {csn 4515  ωcom 7572 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-ext 2730 This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1542  df-ex 1783  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-v 3409  df-dif 3857 This theorem is referenced by:  bnj1098  32268  bnj544  32379  bnj546  32381  bnj594  32397  bnj580  32398  bnj966  32429  bnj967  32430  bnj970  32432  bnj1001  32444  bnj1053  32461  bnj1071  32462  bnj1118  32469  bnj1128  32475  bnj1145  32478
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