Theorem pwne0 5318

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 5317	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4290	1 ⊢ 𝒫 𝐴 ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2956  ∅c0 4279  𝒫 cpw 4557

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2733  ax-nul 5260

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-ne 2957  df-v 3453  df-dif 3902  df-ss 3916  df-nul 4280  df-pw 4559

This theorem is used by:  undefne0  8290  afv20defat  48271