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Metamath Proof Explorer

Theorem 0nnnALT

Description: Alternate proof of 0nnn , which requires ax-pre-mulgt0 but is not based on nnne0 (and which can therefore be used in nnne0ALT ). (Contributed by NM, 25-Aug-1999) (New usage is discouraged.) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	0nnnALT	$⊢ \neg 0 \in ℕ$

Proof

Step	Hyp	Ref	Expression
1		0lt1	$⊢ 0 < 1$
2		nnnlt1	$⊢ 0 \in ℕ \to \neg 0 < 1$
3	1 2	mt2	$⊢ \neg 0 \in ℕ$