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Mirrors > Home > ILE Home > Th. List > dfplq0qs | Unicode version |
Description: Addition on nonnegative fractions. This definition is similar to df-plq0 7049 but expands Q0 (Contributed by Jim Kingdon, 24-Nov-2019.) |
Ref | Expression |
---|---|
dfplq0qs |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-plq0 7049 |
. 2
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2 | df-nq0 7047 |
. . . . . 6
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3 | 2 | eleq2i 2155 |
. . . . 5
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4 | 2 | eleq2i 2155 |
. . . . 5
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5 | 3, 4 | anbi12i 449 |
. . . 4
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6 | 5 | anbi1i 447 |
. . 3
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7 | 6 | oprabbii 5720 |
. 2
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8 | 1, 7 | eqtri 2109 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-oprab 5672 df-nq0 7047 df-plq0 7049 |
This theorem is referenced by: addnnnq0 7071 |
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