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Theorem gboodd 43929
 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 43928 . 2 (𝑍 ∈ GoldbachOdd → 𝑍 ∈ GoldbachOddW )
2 gbowodd 43927 . 2 (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd )
31, 2syl 17 1 (𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2114   Odd codd 43797   GoldbachOddW cgbow 43918   GoldbachOdd cgbo 43919 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 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2795 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2802  df-cleq 2816  df-clel 2895  df-nfc 2965  df-ral 3145  df-rex 3146  df-rab 3149  df-v 3498  df-gbow 43921  df-gbo 43922 This theorem is referenced by: (None)
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