Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dfplq0qs | Unicode version |
Description: Addition on non-negative fractions. This definition is similar to df-plq0 6525 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 6525 | . 2 +Q0 Q0 Q0 ~Q0 ~Q0 ~Q0 | |
2 | df-nq0 6523 | . . . . . 6 Q0 ~Q0 | |
3 | 2 | eleq2i 2104 | . . . . 5 Q0 ~Q0 |
4 | 2 | eleq2i 2104 | . . . . 5 Q0 ~Q0 |
5 | 3, 4 | anbi12i 433 | . . . 4 Q0 Q0 ~Q0 ~Q0 |
6 | 5 | anbi1i 431 | . . 3 Q0 Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
7 | 6 | oprabbii 5560 | . 2 Q0 Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
8 | 1, 7 | eqtri 2060 | 1 +Q0 ~Q0 ~Q0 ~Q0 ~Q0 ~Q0 |
Colors of variables: wff set class |
Syntax hints: wa 97 wceq 1243 wex 1381 wcel 1393 cop 3378 com 4313 cxp 4343 (class class class)co 5512 coprab 5513 coa 5998 comu 5999 cec 6104 cqs 6105 cnpi 6370 ~Q0 ceq0 6384 Q0cnq0 6385 +Q0 cplq0 6387 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-oprab 5516 df-nq0 6523 df-plq0 6525 |
This theorem is referenced by: addnnnq0 6547 |
Copyright terms: Public domain | W3C validator |