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Theorem gboaodd 40179
 Description: An odd Goldbach number is odd. (Contributed by AV, 26-Jul-2020.)
Assertion
Ref Expression
gboaodd (𝑍 ∈ GoldbachOddALTV → 𝑍 ∈ Odd )

Proof of Theorem gboaodd
StepHypRef Expression
1 gboagbo 40178 . 2 (𝑍 ∈ GoldbachOddALTV → 𝑍 ∈ GoldbachOdd )
2 gboodd 40177 . 2 (𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd )
31, 2syl 17 1 (𝑍 ∈ GoldbachOddALTV → 𝑍 ∈ Odd )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1977   Odd codd 40076   GoldbachOdd cgbo 40168   GoldbachOddALTV cgboa 40169 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-rab 2905  df-v 3175  df-gbo 40171  df-gboa 40172 This theorem is referenced by: (None)
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