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Metamath Proof Explorer

Theorem n2dvds3

Description: 2 does not divide 3. That means 3 is odd. (Contributed by AV, 28-Feb-2021) (Proof shortened by Steven Nguyen, 3-May-2023)

		Ref	Expression
	Assertion	n2dvds3	$⊢ \neg 2 ∥ 3$

Step	Hyp	Ref	Expression
1		3halfnz	$⊢ \neg \frac{3}{2} \in ℤ$
2		3z	$⊢ 3 \in ℤ$
3		evend2	$⊢ 3 \in ℤ \to (2 ∥ 3 \leftrightarrow \frac{3}{2} \in ℤ)$
4	2 3	ax-mp	$⊢ 2 ∥ 3 \leftrightarrow \frac{3}{2} \in ℤ$
5	1 4	mtbir	$⊢ \neg 2 ∥ 3$