Theorem pwne0 5304

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 5303	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4298	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2933  ∅c0 4287  𝒫 cpw 4556

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-nul 5253

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ne 2934  df-v 3444  df-dif 3906  df-ss 3920  df-nul 4288  df-pw 4558

This theorem is referenced by:  undefne0  8231  afv20defat  47586