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Mirrors > Home > ILE Home > Th. List > dfmq0qs | Unicode version |
Description: Multiplication on nonnegative fractions. This definition is similar to df-mq0 7377 but expands Q0. (Contributed by Jim Kingdon, 22-Nov-2019.) |
Ref | Expression |
---|---|
dfmq0qs | ·Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mq0 7377 | . 2 ·Q0 Q0 Q0 ~Q0 ~Q0 ~Q0 | |
2 | df-nq0 7374 | . . . . . 6 Q0 ~Q0 | |
3 | 2 | eleq2i 2237 | . . . . 5 Q0 ~Q0 |
4 | 2 | eleq2i 2237 | . . . . 5 Q0 ~Q0 |
5 | 3, 4 | anbi12i 457 | . . . 4 Q0 Q0 ~Q0 ~Q0 |
6 | 5 | anbi1i 455 | . . 3 Q0 Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
7 | 6 | oprabbii 5905 | . 2 Q0 Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
8 | 1, 7 | eqtri 2191 | 1 ·Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wex 1485 wcel 2141 cop 3584 com 4572 cxp 4607 (class class class)co 5850 coprab 5851 comu 6390 cec 6507 cqs 6508 cnpi 7221 ~Q0 ceq0 7235 Q0cnq0 7236 ·Q0 cmq0 7239 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-oprab 5854 df-nq0 7374 df-mq0 7377 |
This theorem is referenced by: mulnnnq0 7399 |
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