Theorem bj-ru

Description: Remove dependency on ax-13 (and df-v ) from Russell's paradox ru expressed with primitive symbols and with a class variable V . Note the more economical use of elissetv instead of isset to avoid use of df-v . (Contributed by BJ, 12-Oct-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-ru	$$⊢\neg \left\{x|\neg x\in x\right\}\in V$$

Proof

Step	Hyp	Ref	Expression
1		bj-ru1	$$⊢\neg \exists yy=\left\{x|\neg x\in x\right\}$$
2		elissetv	$$⊢\left\{x|\neg x\in x\right\}\in V\to \exists yy=\left\{x|\neg x\in x\right\}$$
3	1 2	mto	$$⊢\neg \left\{x|\neg x\in x\right\}\in V$$