Theorem pwne0 5302

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 5301	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4296	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2932  ∅c0 4285  𝒫 cpw 4554

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 2115  ax-9 2123  ax-ext 2708  ax-nul 5251

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 2715  df-cleq 2728  df-clel 2811  df-ne 2933  df-v 3442  df-dif 3904  df-ss 3918  df-nul 4286  df-pw 4556

This theorem is referenced by:  undefne0  8221  afv20defat  47474