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Mathbox for Alexander van der Vekens |
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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 44270 | . 2 ⊢ (𝑍 ∈ GoldbachOddW ↔ (𝑍 ∈ Odd ∧ ∃𝑝 ∈ ℙ ∃𝑞 ∈ ℙ ∃𝑟 ∈ ℙ 𝑍 = ((𝑝 + 𝑞) + 𝑟))) | |
2 | 1 | simplbi 501 | 1 ⊢ (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1538 ∈ wcel 2111 ∃wrex 3107 (class class class)co 7135 + caddc 10529 ℙcprime 16005 Odd codd 44143 GoldbachOddW cgbow 44264 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-rex 3112 df-rab 3115 df-v 3443 df-gbow 44267 |
This theorem is referenced by: gboodd 44275 |
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