Detailed syntax breakdown of Axiom ax-tgoldbachgtOLD
Step | Hyp | Ref
| Expression |
1 | | vm |
. . . . 5
setvar 𝑚 |
2 | 1 | cv 1474 |
. . . 4
class 𝑚 |
3 | | c10 10955 |
. . . . 5
class
10 |
4 | | c2 10947 |
. . . . . 6
class
2 |
5 | | c7 10952 |
. . . . . 6
class
7 |
6 | 4, 5 | cdc 11369 |
. . . . 5
class ;27 |
7 | | cexp 12722 |
. . . . 5
class
↑ |
8 | 3, 6, 7 | co 6549 |
. . . 4
class
(10↑;27) |
9 | | cle 9954 |
. . . 4
class
≤ |
10 | 2, 8, 9 | wbr 4583 |
. . 3
wff 𝑚 ≤ (10↑;27) |
11 | | vn |
. . . . . . 7
setvar 𝑛 |
12 | 11 | cv 1474 |
. . . . . 6
class 𝑛 |
13 | | clt 9953 |
. . . . . 6
class
< |
14 | 2, 12, 13 | wbr 4583 |
. . . . 5
wff 𝑚 < 𝑛 |
15 | | cgboa 40169 |
. . . . . 6
class
GoldbachOddALTV |
16 | 12, 15 | wcel 1977 |
. . . . 5
wff 𝑛 ∈
GoldbachOddALTV |
17 | 14, 16 | wi 4 |
. . . 4
wff (𝑚 < 𝑛 → 𝑛 ∈ GoldbachOddALTV ) |
18 | | codd 40076 |
. . . 4
class
Odd |
19 | 17, 11, 18 | wral 2896 |
. . 3
wff
∀𝑛 ∈ Odd
(𝑚 < 𝑛 → 𝑛 ∈ GoldbachOddALTV ) |
20 | 10, 19 | wa 383 |
. 2
wff (𝑚 ≤ (10↑;27) ∧ ∀𝑛 ∈ Odd (𝑚 < 𝑛 → 𝑛 ∈ GoldbachOddALTV )) |
21 | | cn 10897 |
. 2
class
ℕ |
22 | 20, 1, 21 | wrex 2897 |
1
wff
∃𝑚 ∈
ℕ (𝑚 ≤
(10↑;27) ∧ ∀𝑛 ∈ Odd (𝑚 < 𝑛 → 𝑛 ∈ GoldbachOddALTV )) |