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

Metamath Proof Explorer

Theorem ralndv2

Description: Second example for a theorem about a restricted universal quantification in which the restricting class depends on the bound variable: all subsets of a set are sets. (Contributed by AV, 24-Jun-2023)

Ref Expression
Assertion ralndv2 ⊢ ∀ x ∈ 𝒫 x x ∈ V

Proof

Step Hyp Ref Expression
1 vex ⊢ x ∈ V
2 1 rgenw ⊢ ∀ x ∈ 𝒫 x x ∈ V