![]() |
New Foundations Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > NFE Home > Th. List > ax-typlower | Unicode version |
Description: The type lowering axiom. This axiom eventually sets up both the existence of the sum set and the existence of the range of a relationship. Axiom P6 of [Hailperin] p. 10. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
ax-typlower |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vz |
. . . . 5
![]() ![]() | |
2 | vy |
. . . . 5
![]() ![]() | |
3 | 1, 2 | wel 1711 |
. . . 4
![]() ![]() ![]() ![]() |
4 | vw |
. . . . . . . 8
![]() ![]() | |
5 | 4 | cv 1641 |
. . . . . . 7
![]() ![]() |
6 | 1 | cv 1641 |
. . . . . . . 8
![]() ![]() |
7 | 6 | csn 3738 |
. . . . . . 7
![]() ![]() ![]() ![]() |
8 | 5, 7 | copk 4058 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | vx |
. . . . . . 7
![]() ![]() | |
10 | 9 | cv 1641 |
. . . . . 6
![]() ![]() |
11 | 8, 10 | wcel 1710 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 11, 4 | wal 1540 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 3, 12 | wb 176 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 13, 1 | wal 1540 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 14, 2 | wex 1541 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
This axiom is referenced by: axtyplowerprim 4095 p6exg 4291 |
Copyright terms: Public domain | W3C validator |