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Mirrors > Home > NFE Home > Th. List > ax-sset | Unicode version |
Description: State the axiom of the subset relationship. This axiom guarantees the existence of the Kuratowski relationship representing subset. Slight generalization of axiom P9 of [Hailperin] p. 10. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
ax-sset |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vy |
. . . . . . . 8
![]() ![]() | |
2 | 1 | cv 1641 |
. . . . . . 7
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3 | vz |
. . . . . . . 8
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4 | 3 | cv 1641 |
. . . . . . 7
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5 | 2, 4 | copk 4058 |
. . . . . 6
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6 | vx |
. . . . . . 7
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7 | 6 | cv 1641 |
. . . . . 6
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8 | 5, 7 | wcel 1710 |
. . . . 5
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9 | vw |
. . . . . . . 8
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10 | 9, 1 | wel 1711 |
. . . . . . 7
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11 | 9, 3 | wel 1711 |
. . . . . . 7
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12 | 10, 11 | wi 4 |
. . . . . 6
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13 | 12, 9 | wal 1540 |
. . . . 5
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14 | 8, 13 | wb 176 |
. . . 4
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15 | 14, 3 | wal 1540 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15, 1 | wal 1540 |
. 2
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17 | 16, 6 | wex 1541 |
1
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Colors of variables: wff setvar class |
This axiom is referenced by: axssetprim 4093 ssetkex 4295 |
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