Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Replacement
Theorems requiring empty set existence
pwne0
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0nep0
Metamath Proof Explorer
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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
≠
∅