Mathbox for Alexander van der Vekens |
< Previous
Next >
Nearby theorems |
||
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 44738 | . 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 1542 ∈ wcel 2114 ∃wrex 3054 (class class class)co 7170 + caddc 10618 ℙcprime 16112 Odd codd 44611 GoldbachOddW cgbow 44732 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-ext 2710 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1545 df-ex 1787 df-sb 2075 df-clab 2717 df-cleq 2730 df-clel 2811 df-rex 3059 df-rab 3062 df-v 3400 df-gbow 44735 |
This theorem is referenced by: gboodd 44743 |
Copyright terms: Public domain | W3C validator |