Theorem gbeeven

Description: An even Goldbach number is even. (Contributed by AV, 25-Jul-2020)

	Ref	Expression
Assertion	gbeeven	$$⊢Z\in \mathrm{GoldbachEven}\to Z\in \mathrm{Even}$$

Proof

Step	Hyp	Ref	Expression
1		isgbe	$$⊢Z\in \mathrm{GoldbachEven}\leftrightarrow \left(Z\in \mathrm{Even}\wedge \exists p\in \mathbb{P}\exists q\in \mathbb{P}\left(p\in \mathrm{Odd}\wedge q\in \mathrm{Odd}\wedge Z=p+q\right)\right)$$
2	1	simplbi	$$⊢Z\in \mathrm{GoldbachEven}\to Z\in \mathrm{Even}$$