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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

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