Theorem pwne0 5297

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 5296	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4293	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2929  ∅c0 4282  𝒫 cpw 4549

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 2705  ax-nul 5246

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 2712  df-cleq 2725  df-clel 2808  df-ne 2930  df-v 3439  df-dif 3901  df-ss 3915  df-nul 4283  df-pw 4551

This theorem is referenced by:  undefne0  8215  afv20defat  47357