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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 
|- A. x e. x _V e. x

Proof

Step Hyp Ref Expression
1 elirrv 
 |-  -. x e. x
2 1 pm2.21i 
 |-  ( x e. x -> _V e. x )
3 2 rgen 
 |-  A. x e. x _V e. x