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Theorem pssn0 38991
Description: A proper superset is nonempty. (Contributed by Steven Nguyen, 17-Jul-2022.)
Assertion
Ref Expression
pssn0 (𝐴𝐵𝐵 ≠ ∅)

Proof of Theorem pssn0
StepHypRef Expression
1 npss0 4393 . . 3 ¬ 𝐴 ⊊ ∅
2 psseq2 4062 . . 3 (𝐵 = ∅ → (𝐴𝐵𝐴 ⊊ ∅))
31, 2mtbiri 328 . 2 (𝐵 = ∅ → ¬ 𝐴𝐵)
43necon2ai 3042 1 (𝐴𝐵𝐵 ≠ ∅)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1528  wne 3013  wpss 3934  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-10 2136  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-ne 3014  df-dif 3936  df-in 3940  df-ss 3949  df-pss 3951  df-nul 4289
This theorem is referenced by:  xppss12  38993
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