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Metamath Proof Explorer

Theorem vsn

Description: The singleton of the universal class is the empty set. (Contributed by Zhi Wang, 19-Sep-2024)

		Ref	Expression
	Assertion	vsn	⊢ { V } = ∅

Step	Hyp	Ref	Expression
1		vprc	⊢ ¬ V ∈ V
2		snprc	⊢ ( ¬ V ∈ V ↔ { V } = ∅ )
3	1 2	mpbi	⊢ { V } = ∅