| Mathbox for Alexander van der Vekens |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > gboodd | Structured version Visualization version GIF version | ||
| Description: An odd Goldbach number is odd. (Contributed by AV, 26-Jul-2020.) |
| Ref | Expression |
|---|---|
| gboodd | ⊢ (𝑍 ∈ GoldbachOdd → 𝑍 ∈ Odd ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | gbogbow 47743 | . 2 ⊢ (𝑍 ∈ GoldbachOdd → 𝑍 ∈ GoldbachOddW ) | |
| 2 | gbowodd 47742 | . 2 ⊢ (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd ) | |
| 3 | 1, 2 | syl 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) |
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