Theorem pwuninel2

Description: Direct proof of pwuninel avoiding functions and thus several ZF axioms. (Contributed by Stefan O'Rear, 22-Feb-2015)

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

Proof

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