Theorem gbowodd

Description: A weak odd Goldbach number is odd. (Contributed by AV, 25-Jul-2020)

	Ref	Expression
Assertion	gbowodd	$$⊢Z\in \mathrm{GoldbachOddW}\to Z\in \mathrm{Odd}$$

Proof

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