Theorem pwne0 5329

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 5328	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4298	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2958  ∅c0 4287  𝒫 cpw 4563

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-nul 5270

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-ne 2959  df-v 3457  df-dif 3909  df-ss 3923  df-nul 4288  df-pw 4565

This theorem is referenced by:  undefne0  8277  afv20defat  47952