Metamath Proof Explorer


Theorem pwne0

Description: A power class is never empty. (Contributed by NM, 3-Sep-2018)

Ref Expression
Assertion pwne0 𝒫 𝐴 ≠ ∅

Proof

Step Hyp Ref Expression
1 0elpw ∅ ∈ 𝒫 𝐴
2 1 ne0ii 𝒫 𝐴 ≠ ∅