Users' Mathboxes Mathbox for Alexander van der Vekens < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  gboodd Structured version   Visualization version   GIF version

Theorem gboodd 47744
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 47743 . 2 (𝑍 ∈ GoldbachOdd → 𝑍 ∈ GoldbachOddW )
2 gbowodd 47742 . 2 (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd )
31, 2syl 17 1 (𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108   Odd codd 47612   GoldbachOddW cgbow 47733   GoldbachOdd cgbo 47734
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 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rex 3071  df-rab 3437  df-v 3482  df-gbow 47736  df-gbo 47737
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator