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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 46034 | . 2 ⊢ (𝑍 ∈ GoldbachOddW ↔ (𝑍 ∈ Odd ∧ ∃𝑝 ∈ ℙ ∃𝑞 ∈ ℙ ∃𝑟 ∈ ℙ 𝑍 = ((𝑝 + 𝑞) + 𝑟))) | |
2 | 1 | simplbi 499 | 1 ⊢ (𝑍 ∈ GoldbachOddW → 𝑍 ∈ Odd ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1542 ∈ wcel 2107 ∃wrex 3070 (class class class)co 7361 + caddc 11062 ℙcprime 16555 Odd codd 45907 GoldbachOddW cgbow 46028 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-rex 3071 df-rab 3407 df-v 3449 df-gbow 46031 |
This theorem is referenced by: gboodd 46039 |
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