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	⊢ ¬ 0 ∈ ℕ

Proof

Step	Hyp	Ref	Expression
1		0lt1	⊢ 0 < 1
2		nnnlt1	⊢ ( 0 ∈ ℕ → ¬ 0 < 1 )
3	1 2	mt2	⊢ ¬ 0 ∈ ℕ