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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 ≠ ∅