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Theorem n0ii 4329
Description: If a class has elements, then it is not empty. Inference associated with n0i 4326. (Contributed by BJ, 15-Jul-2021.)
Hypothesis
Ref Expression
n0ii.1 𝐴𝐵
Assertion
Ref Expression
n0ii ¬ 𝐵 = ∅

Proof of Theorem n0ii
StepHypRef Expression
1 n0ii.1 . 2 𝐴𝐵
2 n0i 4326 . 2 (𝐴𝐵 → ¬ 𝐵 = ∅)
31, 2ax-mp 5 1 ¬ 𝐵 = ∅
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1533  wcel 2098  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-8 2100  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-clel 2802  df-dif 3944  df-nul 4316
This theorem is referenced by:  iin0  5351  snsn0non  6480  tfrlem16  8389  hon0  31540  dmadjrnb  31653  bnj98  34396  prv0  34938  dvnprodlem3  45209
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