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Metamath Proof Explorer

Theorem neutru

Description: There does not exist exactly one set such that T. is true. (Contributed by Anthony Hart, 13-Sep-2011)

		Ref	Expression
	Assertion	neutru	$⊢ \neg \exists! x ⊤$

Step	Hyp	Ref	Expression
1		nexntru	$⊢ \neg \exists x \neg ⊤$
2		eunex	$⊢ \exists! x ⊤ \to \exists x \neg ⊤$
3	1 2	mto	$⊢ \neg \exists! x ⊤$