Theorem gboodd 47738

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 47737	. 2 ⊢ (𝑍 ∈ GoldbachOdd → 𝑍 ∈ GoldbachOddW )
2		gbowodd 47736	. 2 ⊢ (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd )
3	1, 2	syl 17	1 ⊢ (𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd )

Syntax hints:   → wi 4   ∈ wcel 2109   Odd codd 47606   GoldbachOddW cgbow 47727   GoldbachOdd cgbo 47728

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-rex 3062  df-rab 3421  df-v 3466  df-gbow 47730  df-gbo 47731

This theorem is referenced by: (None)