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Mirrors > Home > ILE Home > Th. List > dfplq0qs | Unicode version |
Description: Addition on non-negative fractions. This definition is similar to df-plq0 6617 but expands Q0 (Contributed by Jim Kingdon, 24-Nov-2019.) |
Ref | Expression |
---|---|
dfplq0qs | +Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-plq0 6617 | . 2 +Q0 Q0 Q0 ~Q0 ~Q0 ~Q0 | |
2 | df-nq0 6615 | . . . . . 6 Q0 ~Q0 | |
3 | 2 | eleq2i 2145 | . . . . 5 Q0 ~Q0 |
4 | 2 | eleq2i 2145 | . . . . 5 Q0 ~Q0 |
5 | 3, 4 | anbi12i 447 | . . . 4 Q0 Q0 ~Q0 ~Q0 |
6 | 5 | anbi1i 445 | . . 3 Q0 Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
7 | 6 | oprabbii 5580 | . 2 Q0 Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
8 | 1, 7 | eqtri 2101 | 1 +Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
Colors of variables: wff set class |
Syntax hints: wa 102 wceq 1284 wex 1421 wcel 1433 cop 3401 com 4331 cxp 4361 (class class class)co 5532 coprab 5533 coa 6021 comu 6022 cec 6127 cqs 6128 cnpi 6462 ~Q0 ceq0 6476 Q0cnq0 6477 +Q0 cplq0 6479 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-oprab 5536 df-nq0 6615 df-plq0 6617 |
This theorem is referenced by: addnnnq0 6639 |
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