Theorem 2evenALTV

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

	Ref	Expression
Assertion	2evenALTV	$$⊢2\in \mathrm{Even}$$

Proof

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