Theorem gboodd 47767

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

Assertion

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

Proof of Theorem gboodd

Step	Hyp	Ref	Expression
1		gbogbow 47766	. 2 ⊢ (𝑍 ∈ GoldbachOdd → 𝑍 ∈ GoldbachOddW )
2		gbowodd 47765	. 2 ⊢ (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd )
3	1, 2	syl 17	1 ⊢ (𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd )

Syntax hints:   → wi 4   ∈ wcel 2110   Odd codd 47635   GoldbachOddW cgbow 47756   GoldbachOdd cgbo 47757

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2112  ax-9 2120  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2722  df-clel 2804  df-rex 3055  df-rab 3394  df-v 3436  df-gbow 47759  df-gbo 47760

This theorem is referenced by: (None)