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Theorem gboodd 41416
 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
StepHypRef Expression
1 gbogbow 41415 . 2 (𝑍 ∈ GoldbachOdd → 𝑍 ∈ GoldbachOddW )
2 gbowodd 41414 . 2 (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd )
31, 2syl 17 1 (𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1989   Odd codd 41309   GoldbachOddW cgbow 41405   GoldbachOdd cgbo 41406 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-9 1998  ax-10 2018  ax-11 2033  ax-12 2046  ax-13 2245  ax-ext 2601 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1485  df-ex 1704  df-nf 1709  df-sb 1880  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2752  df-ral 2916  df-rex 2917  df-rab 2920  df-v 3200  df-gbow 41408  df-gbo 41409 This theorem is referenced by: (None)
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