This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem halfnz

Description: One-half is not an integer. (Contributed by NM, 31-Jul-2004)

		Ref	Expression
	Assertion	halfnz	$⊢ \neg \frac{1}{2} \in ℤ$

Step	Hyp	Ref	Expression
1		2re	$⊢ 2 \in ℝ$
2		1lt2	$⊢ 1 < 2$
3		recnz	$⊢ (2 \in ℝ \land 1 < 2) \to \neg \frac{1}{2} \in ℤ$
4	1 2 3	mp2an	$⊢ \neg \frac{1}{2} \in ℤ$