Theorem pwne0 5292

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 5291	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4279	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2935  ∅c0 4268  𝒫 cpw 4536

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712  ax-nul 5235

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-ne 2936  df-v 3434  df-dif 3893  df-ss 3907  df-nul 4269  df-pw 4538

This theorem is referenced by:  undefne0  8226  afv20defat  47702