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Mirrors > Home > MPE Home > Th. List > df-plp | Structured version Visualization version Unicode version |
Description: Define addition on positive reals. This is a "temporary" set used in the construction of complex numbers df-c 9545, and is intended to be used only by the construction. From Proposition 9-3.5 of [Gleason] p. 123. (Contributed by NM, 18-Nov-1995.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-plp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpp 9286 |
. 2
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2 | vx |
. . 3
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3 | vy |
. . 3
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4 | cnp 9284 |
. . 3
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5 | vw |
. . . . . . . 8
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6 | 5 | cv 1443 |
. . . . . . 7
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7 | vv |
. . . . . . . . 9
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8 | 7 | cv 1443 |
. . . . . . . 8
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9 | vu |
. . . . . . . . 9
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10 | 9 | cv 1443 |
. . . . . . . 8
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11 | cplq 9280 |
. . . . . . . 8
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12 | 8, 10, 11 | co 6290 |
. . . . . . 7
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13 | 6, 12 | wceq 1444 |
. . . . . 6
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14 | 3 | cv 1443 |
. . . . . 6
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15 | 13, 9, 14 | wrex 2738 |
. . . . 5
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16 | 2 | cv 1443 |
. . . . 5
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17 | 15, 7, 16 | wrex 2738 |
. . . 4
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18 | 17, 5 | cab 2437 |
. . 3
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19 | 2, 3, 4, 4, 18 | cmpt2 6292 |
. 2
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20 | 1, 19 | wceq 1444 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: plpv 9435 dmplp 9437 addclprlem2 9442 addclpr 9443 addasspr 9447 distrlem1pr 9450 distrlem4pr 9451 distrlem5pr 9452 ltaddpr 9459 ltexprlem6 9466 ltexprlem7 9467 |
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