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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 7238 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 7238 | . 2 +Q0 Q0 Q0 ~Q0 ~Q0 ~Q0 | |
2 | df-nq0 7236 | . . . . . 6 Q0 ~Q0 | |
3 | 2 | eleq2i 2206 | . . . . 5 Q0 ~Q0 |
4 | 2 | eleq2i 2206 | . . . . 5 Q0 ~Q0 |
5 | 3, 4 | anbi12i 455 | . . . 4 Q0 Q0 ~Q0 ~Q0 |
6 | 5 | anbi1i 453 | . . 3 Q0 Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
7 | 6 | oprabbii 5826 | . 2 Q0 Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
8 | 1, 7 | eqtri 2160 | 1 +Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wex 1468 wcel 1480 cop 3530 com 4504 cxp 4537 (class class class)co 5774 coprab 5775 coa 6310 comu 6311 cec 6427 cqs 6428 cnpi 7083 ~Q0 ceq0 7097 Q0cnq0 7098 +Q0 cplq0 7100 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-oprab 5778 df-nq0 7236 df-plq0 7238 |
This theorem is referenced by: addnnnq0 7260 |
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