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Mirrors > Home > NFE Home > Th. List > ax-sn | Unicode version |
Description: The singleton axiom. This axiom sets up the existence of a singleton set. This appears to have been an oversight on Hailperin's part, as it is needed to prove the properties of Kuratowski ordered pairs. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
ax-sn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vz |
. . . . 5
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2 | vy |
. . . . 5
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3 | 1, 2 | wel 1711 |
. . . 4
![]() ![]() ![]() ![]() |
4 | vx |
. . . . 5
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5 | 1, 4 | weq 1643 |
. . . 4
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6 | 3, 5 | wb 176 |
. . 3
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7 | 6, 1 | wal 1540 |
. 2
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8 | 7, 2 | wex 1541 |
1
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Colors of variables: wff setvar class |
This axiom is referenced by: snex 4112 |
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