Theorem pwne0 5248

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 5247	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4252	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2940  ∅c0 4237  𝒫 cpw 4513

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708  ax-nul 5199

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-v 3410  df-dif 3869  df-in 3873  df-ss 3883  df-nul 4238  df-pw 4515

This theorem is referenced by:  undefne0  8021  afv20defat  44396