Theorem pwne0 5329

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 5328	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4297	1 ⊢ 𝒫 𝐴 ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2960  ∅c0 4286  𝒫 cpw 4564

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737  ax-nul 5271

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-ne 2961  df-v 3459  df-dif 3909  df-ss 3923  df-nul 4287  df-pw 4566

This theorem is used by:  undefne0  8278  afv20defat  48002