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Theorem pssn0 39427
 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 4353 . . 3 ¬ 𝐴 ⊊ ∅
2 psseq2 4016 . . 3 (𝐵 = ∅ → (𝐴𝐵𝐴 ⊊ ∅))
31, 2mtbiri 330 . 2 (𝐵 = ∅ → ¬ 𝐴𝐵)
43necon2ai 3016 1 (𝐴𝐵𝐵 ≠ ∅)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538   ≠ wne 2987   ⊊ wpss 3882  ∅c0 4243 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-ne 2988  df-v 3443  df-dif 3884  df-in 3888  df-ss 3898  df-pss 3900  df-nul 4244 This theorem is referenced by:  xppss12  39429
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