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ThmDex – An index of mathematical definitions, results, and conjectures.
Result R1034 on D80: Power set
Power set is closed under unions
Formulation 0
Let X be a D11: Set.
Let Ej be a D11: Set for each jJ.
Then jJ:EjP(X)jJEjP(X)
Formulation 1
Let X be a D11: Set.
Let Ej be a D11: Set for each jJ.
Then jJ:EjXjJEjX
Proofs
Proof 0
Let X be a D11: Set.
Let Ej be a D11: Set for each jJ.
Corollary to R2071: Isotonicity of set union.