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Metamath Proof Explorer

Theorem pwuninel2

Description: Proof of pwuninel under the assumption that the union of the given class is a set, avoiding ax-pr and ax-un . (Contributed by Stefan O'Rear, 22-Feb-2015)

		Ref	Expression
	Assertion	pwuninel2	$⊢ ⋃ A \in V \to \neg 𝒫 ⋃ A \in A$

Proof

Step	Hyp	Ref	Expression
1		pwnss	$⊢ ⋃ A \in V \to \neg 𝒫 ⋃ A \subseteq ⋃ A$
2		elssuni	$⊢ 𝒫 ⋃ A \in A \to 𝒫 ⋃ A \subseteq ⋃ A$
3	1 2	nsyl	$⊢ ⋃ A \in V \to \neg 𝒫 ⋃ A \in A$