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Mirrors > Home > ILE Home > Th. List > ax-precex | Unicode version |
Description: Existence of reciprocal of positive real number. Axiom for real and complex numbers, justified by Theorem axprecex 7879. (Contributed by Jim Kingdon, 6-Feb-2020.) |
Ref | Expression |
---|---|
ax-precex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
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2 | cr 7810 |
. . . 4
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3 | 1, 2 | wcel 2148 |
. . 3
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4 | cc0 7811 |
. . . 4
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5 | cltrr 7815 |
. . . 4
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6 | 4, 1, 5 | wbr 4004 |
. . 3
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7 | 3, 6 | wa 104 |
. 2
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8 | vx |
. . . . . 6
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9 | 8 | cv 1352 |
. . . . 5
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10 | 4, 9, 5 | wbr 4004 |
. . . 4
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11 | cmul 7816 |
. . . . . 6
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12 | 1, 9, 11 | co 5875 |
. . . . 5
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13 | c1 7812 |
. . . . 5
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14 | 12, 13 | wceq 1353 |
. . . 4
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15 | 10, 14 | wa 104 |
. . 3
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16 | 15, 8, 2 | wrex 2456 |
. 2
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17 | 7, 16 | wi 4 |
1
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Colors of variables: wff set class |
This axiom is referenced by: recexre 8535 recexgt0 8537 |
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