Theorem pwne0 5298

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 5297	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4284	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2932  ∅c0 4273  𝒫 cpw 4541

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 2708  ax-nul 5241

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 2715  df-cleq 2728  df-clel 2811  df-ne 2933  df-v 3431  df-dif 3892  df-ss 3906  df-nul 4274  df-pw 4543

This theorem is referenced by:  undefne0  8229  afv20defat  47680