Theorem gboodd

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

	Ref	Expression
Assertion	gboodd	⊢ ( 𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd )

Proof

Step	Hyp	Ref	Expression
1		gbogbow	⊢ ( 𝑍 ∈ GoldbachOdd → 𝑍 ∈ GoldbachOddW )
2		gbowodd	⊢ ( 𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd )
3	1 2	syl	⊢ ( 𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd )