Theorem pwne0 5257

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 5256	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4303	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 3016  ∅c0 4291  𝒫 cpw 4539

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 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2793  ax-nul 5210

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-ne 3017  df-v 3496  df-dif 3939  df-in 3943  df-ss 3952  df-nul 4292  df-pw 4541

This theorem is referenced by:  undefne0  7945  afv20defat  43451