This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	⊢ ∀ 𝑥 ∈ 𝑥 V ∈ 𝑥

Proof

Step	Hyp	Ref	Expression
1		elirrv	⊢ ¬ 𝑥 ∈ 𝑥
2	1	pm2.21i	⊢ ( 𝑥 ∈ 𝑥 → V ∈ 𝑥 )
3	2	rgen	⊢ ∀ 𝑥 ∈ 𝑥 V ∈ 𝑥