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

Step	Hyp	Ref	Expression
1		gbogbow 43928	. 2 ⊢ (𝑍 ∈ GoldbachOdd → 𝑍 ∈ GoldbachOddW )
2		gbowodd 43927	. 2 ⊢ (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd )
3	1, 2	syl 17	1 ⊢ (𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd )

Syntax hints:   → wi 4   ∈ wcel 2113   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 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-ral 3146  df-rex 3147  df-rab 3150  df-v 3499  df-gbow 43921  df-gbo 43922

This theorem is referenced by: (None)