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Mirrors > Home > ILE Home > Th. List > Mathboxes > ax-sscoll | Unicode version |
Description: Axiom scheme of subset collection. It is stated with all possible disjoint variable conditions, to show that this weak form is sufficient. (Contributed by BJ, 5-Oct-2019.) |
Ref | Expression |
---|---|
ax-sscoll |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . . . . . . 8 | |
2 | vy | . . . . . . . 8 | |
3 | vb | . . . . . . . . 9 | |
4 | 3 | cv 1283 | . . . . . . . 8 |
5 | 1, 2, 4 | wrex 2349 | . . . . . . 7 |
6 | vx | . . . . . . 7 | |
7 | va | . . . . . . . 8 | |
8 | 7 | cv 1283 | . . . . . . 7 |
9 | 5, 6, 8 | wral 2348 | . . . . . 6 |
10 | vd | . . . . . . . . . 10 | |
11 | 2, 10 | wel 1434 | . . . . . . . . 9 |
12 | 1, 6, 8 | wrex 2349 | . . . . . . . . 9 |
13 | 11, 12 | wb 103 | . . . . . . . 8 |
14 | 13, 2 | wal 1282 | . . . . . . 7 |
15 | vc | . . . . . . . 8 | |
16 | 15 | cv 1283 | . . . . . . 7 |
17 | 14, 10, 16 | wrex 2349 | . . . . . 6 |
18 | 9, 17 | wi 4 | . . . . 5 |
19 | vz | . . . . 5 | |
20 | 18, 19 | wal 1282 | . . . 4 |
21 | 20, 15 | wex 1421 | . . 3 |
22 | 21, 3 | wal 1282 | . 2 |
23 | 22, 7 | wal 1282 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: sscoll2 10783 |
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