Theorem gboodd

Description: An odd Goldbach number is odd. (Contributed by AV, 26-Jul-2020)

	Ref	Expression
Assertion	gboodd	$$⊢Z\in \mathrm{GoldbachOdd}\to Z\in \mathrm{Odd}$$

Proof

Step	Hyp	Ref	Expression
1		gbogbow	$$⊢Z\in \mathrm{GoldbachOdd}\to Z\in \mathrm{GoldbachOddW}$$
2		gbowodd	$$⊢Z\in \mathrm{GoldbachOddW}\to Z\in \mathrm{Odd}$$
3	1 2	syl	$$⊢Z\in \mathrm{GoldbachOdd}\to Z\in \mathrm{Odd}$$