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Theorem bj-n0i 34159
Description: Inference associated with n0 4307. Shortens 2ndcdisj 21992 (2888>2878), notzfaus 5253 (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 4307 . 2 (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥𝐴)
31, 2mpbi 231 1 𝑥 𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wex 1771  wcel 2105  wne 3013  c0 4288
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-ne 3014  df-dif 3936  df-nul 4289
This theorem is referenced by: (None)
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