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Metamath Proof Explorer

Theorem 0ntop

Description: The empty set is not a topology. (Contributed by FL, 1-Jun-2008)

		Ref	Expression
	Assertion	0ntop	⊢ ¬ ∅ ∈ Top

Step	Hyp	Ref	Expression
1		noel	⊢ ¬ ∅ ∈ ∅
2		0opn	⊢ ( ∅ ∈ Top → ∅ ∈ ∅ )
3	1 2	mto	⊢ ¬ ∅ ∈ Top