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Mirrors > Home > MPE Home > Th. List > Mathboxes > gbowodd | Structured version Visualization version GIF version |
Description: A weak odd Goldbach number is odd. (Contributed by AV, 25-Jul-2020.) |
Ref | Expression |
---|---|
gbowodd | ⊢ (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isgbow 43924 | . 2 ⊢ (𝑍 ∈ GoldbachOddW ↔ (𝑍 ∈ Odd ∧ ∃𝑝 ∈ ℙ ∃𝑞 ∈ ℙ ∃𝑟 ∈ ℙ 𝑍 = ((𝑝 + 𝑞) + 𝑟))) | |
2 | 1 | simplbi 500 | 1 ⊢ (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 ∈ wcel 2114 ∃wrex 3141 (class class class)co 7158 + caddc 10542 ℙcprime 16017 Odd codd 43797 GoldbachOddW cgbow 43918 |
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-rex 3146 df-rab 3149 df-v 3498 df-gbow 43921 |
This theorem is referenced by: gboodd 43929 |
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