Theorem pwne0 5222

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 5221	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4253	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2987  ∅c0 4243  𝒫 cpw 4497

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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-nul 5174

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-ne 2988  df-v 3443  df-dif 3884  df-in 3888  df-ss 3898  df-nul 4244  df-pw 4499

This theorem is referenced by:  undefne0  7928  afv20defat  43788