Theorem gbowodd

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

	Ref	Expression
Assertion	gbowodd	⊢ ( 𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd )

Proof

Step	Hyp	Ref	Expression
1		isgbow	⊢ ( 𝑍 ∈ GoldbachOddW ↔ ( 𝑍 ∈ Odd ∧ ∃ 𝑝 ∈ ℙ ∃ 𝑞 ∈ ℙ ∃ 𝑟 ∈ ℙ 𝑍 = ( ( 𝑝 + 𝑞 ) + 𝑟 ) ) )
2	1	simplbi	⊢ ( 𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd )