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Theorem bj-n0i 33512
 Description: Inference associated with n0 4159. Shortens 2ndcdisj 21672 (2888>2878), notzfaus 5076 (264>253). (Contributed by BJ, 22-Apr-2019.)
Hypothesis
Ref Expression
bj-n0i.1 𝐴 ≠ ∅
Assertion
Ref Expression
bj-n0i 𝑥 𝑥𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem bj-n0i
StepHypRef Expression
1 bj-n0i.1 . 2 𝐴 ≠ ∅
2 n0 4159 . 2 (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥𝐴)
31, 2mpbi 222 1 𝑥 𝑥𝐴
 Colors of variables: wff setvar class Syntax hints:  ∃wex 1823   ∈ wcel 2107   ≠ wne 2969  ∅c0 4141 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-ext 2754 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-ne 2970  df-dif 3795  df-nul 4142 This theorem is referenced by: (None)
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