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Theorem pwne0 4610
 Description: A power class is never empty. (Contributed by NM, 3-Sep-2018.)
Assertion
Ref Expression
pwne0

Proof of Theorem pwne0
StepHypRef Expression
1 noel 3782 . 2
2 0elpw 4609 . . . 4
3 eleq2 2533 . . . 4
42, 3mpbii 211 . . 3
54necon3bi 2689 . 2
61, 5ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wceq 1374   wcel 1762   wne 2655  c0 3778  cpw 4003 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438  ax-nul 4569 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-v 3108  df-dif 3472  df-in 3476  df-ss 3483  df-nul 3779  df-pw 4005 This theorem is referenced by:  undefne0  6998
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