Theorem pwne0 5295

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 5294	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4294	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2928  ∅c0 4283  𝒫 cpw 4550

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-nul 5244

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-ne 2929  df-v 3438  df-dif 3905  df-ss 3919  df-nul 4284  df-pw 4552

This theorem is referenced by:  undefne0  8209  afv20defat  47269