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Metamath Proof Explorer

Theorem nvel

Description: The universal class does not belong to any class. (Contributed by FL, 31-Dec-2006)

Ref Expression
Assertion nvel ⊢ ¬ V ∈ A

Proof

Step Hyp Ref Expression
1 vprc ⊢ ¬ V ∈ V
2 elex ⊢ V ∈ A → V ∈ V
3 1 2 mto ⊢ ¬ V ∈ A