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Axiom ax-bgbltosilva 40024
Description: The binary Goldbach conjecture is valid for all even numbers less than or equal to 4x10^18, see result of [OeSilva] p. ?. Temporarily provided as "axiom". (Contributed by AV, 3-Aug-2020.) (Revised by AV, 9-Sep-2021.)
Assertion
Ref Expression
ax-bgbltosilva ((𝑁 ∈ Even ∧ 4 < 𝑁𝑁 ≤ (4 · (10↑18))) → 𝑁 ∈ GoldbachEven )

Detailed syntax breakdown of Axiom ax-bgbltosilva
StepHypRef Expression
1 cN . . . 4 class 𝑁
2 ceven 39873 . . . 4 class Even
31, 2wcel 1976 . . 3 wff 𝑁 ∈ Even
4 c4 10919 . . . 4 class 4
5 clt 9930 . . . 4 class <
64, 1, 5wbr 4577 . . 3 wff 4 < 𝑁
7 c1 9793 . . . . . . 7 class 1
8 cc0 9792 . . . . . . 7 class 0
97, 8cdc 11325 . . . . . 6 class 10
10 c8 10923 . . . . . . 7 class 8
117, 10cdc 11325 . . . . . 6 class 18
12 cexp 12677 . . . . . 6 class
139, 11, 12co 6527 . . . . 5 class (10↑18)
14 cmul 9797 . . . . 5 class ·
154, 13, 14co 6527 . . . 4 class (4 · (10↑18))
16 cle 9931 . . . 4 class
171, 15, 16wbr 4577 . . 3 wff 𝑁 ≤ (4 · (10↑18))
183, 6, 17w3a 1030 . 2 wff (𝑁 ∈ Even ∧ 4 < 𝑁𝑁 ≤ (4 · (10↑18)))
19 cgbe 39965 . . 3 class GoldbachEven
201, 19wcel 1976 . 2 wff 𝑁 ∈ GoldbachEven
2118, 20wi 4 1 wff ((𝑁 ∈ Even ∧ 4 < 𝑁𝑁 ≤ (4 · (10↑18))) → 𝑁 ∈ GoldbachEven )
Colors of variables: wff setvar class
This axiom is referenced by:  bgoldbachlt  40025  tgblthelfgott  40027
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