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Theorem bj-n0i 36323
Description: Inference associated with n0 4339. Shortens 2ndcdisj 23284 (2888>2878), notzfaus 5352 (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 4339 . 2 (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥𝐴)
31, 2mpbi 229 1 𝑥 𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wex 1773  wcel 2098  wne 2932  c0 4315
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-9 2108  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-ne 2933  df-dif 3944  df-nul 4316
This theorem is referenced by: (None)
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