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Theorem n0ii 3375
 Description: If a class has elements, then it is not empty. Inference associated with n0i 3372. (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 3372 . 2 (𝐴𝐵 → ¬ 𝐵 = ∅)
31, 2ax-mp 5 1 ¬ 𝐵 = ∅
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   = wceq 1332   ∈ wcel 1481  ∅c0 3367 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-dif 3077  df-nul 3368 This theorem is referenced by: (None)
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