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Metamath Proof Explorer

Theorem intv

Description: The intersection of the universal class is empty. (Contributed by NM, 11-Sep-2008)

		Ref	Expression
	Assertion	intv	⊢ ∩ V = ∅

Step	Hyp	Ref	Expression
1		0ex	⊢ ∅ ∈ V
2		int0el	⊢ ( ∅ ∈ V → ∩ V = ∅ )
3	1 2	ax-mp	⊢ ∩ V = ∅