Theorem pwne0 5356

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 5355	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4343	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2939  ∅c0 4332  𝒫 cpw 4599

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-nul 5305

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-ne 2940  df-v 3481  df-dif 3953  df-ss 3967  df-nul 4333  df-pw 4601

This theorem is referenced by:  undefne0  8305  afv20defat  47249