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 ≠ ∅