Theorem ralndv1

Description: Example for a theorem about a restricted universal quantification in which the restricting class depends on (actually is) the bound variable: All sets containing themselves contain the universal class. (Contributed by AV, 24-Jun-2023)

	Ref	Expression
Assertion	ralndv1	$$⊢\forall x\in x\mathrm{V}\in x$$

Proof

Step	Hyp	Ref	Expression
1		elirrv	$$⊢\neg x\in x$$
2	1	pm2.21i	$$⊢x\in x\to \mathrm{V}\in x$$
3	2	rgen	$$⊢\forall x\in x\mathrm{V}\in x$$