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Mirrors > Home > ILE Home > Th. List > ax-pre-apti | Unicode version |
Description: Apartness of reals is tight. Axiom for real and complex numbers, justified by Theorem axpre-apti 7862. (Contributed by Jim Kingdon, 29-Jan-2020.) |
Ref | Expression |
---|---|
ax-pre-apti |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
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2 | cr 7788 |
. . . 4
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3 | 1, 2 | wcel 2148 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 2148 |
. . 3
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6 | cltrr 7793 |
. . . . . 6
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7 | 1, 4, 6 | wbr 4000 |
. . . . 5
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8 | 4, 1, 6 | wbr 4000 |
. . . . 5
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9 | 7, 8 | wo 708 |
. . . 4
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10 | 9 | wn 3 |
. . 3
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11 | 3, 5, 10 | w3a 978 |
. 2
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12 | 1, 4 | wceq 1353 |
. 2
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13 | 11, 12 | wi 4 |
1
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Colors of variables: wff set class |
This axiom is referenced by: axapti 8005 |
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