Metamath Proof Explorer

Theorem 2evenALTV

Description: 2 is an even number. (Contributed by AV, 12-Feb-2020) (Revised by AV, 18-Jun-2020)

		Ref	Expression
	Assertion	2evenALTV	$⊢ 2 \in Even$

Step	Hyp	Ref	Expression
1		2z	$⊢ 2 \in ℤ$
2		2div2e1	$⊢ \frac{2}{2} = 1$
3		1z	$⊢ 1 \in ℤ$
4	2 3	eqeltri	$⊢ \frac{2}{2} \in ℤ$
5		iseven	$⊢ 2 \in Even \leftrightarrow (2 \in ℤ \land \frac{2}{2} \in ℤ)$
6	1 4 5	mpbir2an	$⊢ 2 \in Even$