Theorem pwne0 5310

Description: A power class is never empty. (Contributed by NM, 3-Sep-2018.)

Assertion

Ref	Expression
pwne0	⊢ 𝒫 𝐴 ≠ ∅

Proof of Theorem pwne0

Step	Hyp	Ref	Expression
1		0elpw 5309	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4295	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2941  ∅c0 4280  𝒫 cpw 4558

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-nul 5261

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-ne 2942  df-v 3445  df-dif 3911  df-in 3915  df-ss 3925  df-nul 4281  df-pw 4560

This theorem is referenced by:  undefne0  8206  afv20defat  45396