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 4289	1 ⊢ 𝒫 𝐴 ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2955  ∅c0 4278  𝒫 cpw 4556

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-nul 5259

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-v 3452  df-ss 3896  df-dif 4047  df-nul 4279  df-pw 4558

This theorem is used by:  undefne0  8301  afv20defat  48396