Theorem pwne0 5317

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 5316	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4299	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2960  ∅c0 4288  𝒫 cpw 4558

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737  ax-nul 5260

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1566  df-fal 1576  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-ne 2961  df-v 3459  df-dif 3910  df-ss 3924  df-nul 4289  df-pw 4560

This theorem is referenced by:  undefne0  8264  afv20defat  47825