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Mirrors > Home > NFE Home > Th. List > df-sfin | Unicode version |
Description: Define the finite S relationship. This relationship encapsulates the idea of being a "smaller" number than . Definition from [Rosser] p. 530. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
df-sfin | Sfin Nn Nn 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cM | . . 3 | |
2 | cN | . . 3 | |
3 | 1, 2 | wsfin 4438 | . 2 Sfin |
4 | cnnc 4373 | . . . 4 Nn | |
5 | 1, 4 | wcel 1710 | . . 3 Nn |
6 | 2, 4 | wcel 1710 | . . 3 Nn |
7 | va | . . . . . . . 8 | |
8 | 7 | cv 1641 | . . . . . . 7 |
9 | 8 | cpw1 4135 | . . . . . 6 1 |
10 | 9, 1 | wcel 1710 | . . . . 5 1 |
11 | 8 | cpw 3722 | . . . . . 6 |
12 | 11, 2 | wcel 1710 | . . . . 5 |
13 | 10, 12 | wa 358 | . . . 4 1 |
14 | 13, 7 | wex 1541 | . . 3 1 |
15 | 5, 6, 14 | w3a 934 | . 2 Nn Nn 1 |
16 | 3, 15 | wb 176 | 1 Sfin Nn Nn 1 |
Colors of variables: wff setvar class |
This definition is referenced by: srelk 4524 sfineq1 4526 sfineq2 4527 sfin01 4528 sfin112 4529 sfindbl 4530 sfintfin 4532 sfinltfin 4535 sfin111 4536 spfinsfincl 4539 vfinspnn 4541 1cvsfin 4542 vfinspsslem1 4550 |
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