![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > adddird | Unicode version |
Description: Distributive law (right-distributivity). (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
addcld.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
addcld.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
addassd.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
adddird |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcld.1 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | addcld.2 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | addassd.3 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | adddir 7962 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 1, 2, 3, 4 | syl3anc 1248 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 ax-addcl 7921 ax-mulcom 7926 ax-distr 7929 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-rex 2471 df-v 2751 df-un 3145 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-iota 5190 df-fv 5236 df-ov 5891 |
This theorem is referenced by: adddirp1d 7998 joinlmuladdmuld 7999 1p1times 8105 recextlem1 8622 divdirap 8668 subsq 10641 subsq2 10642 binom2 10646 binom3 10652 remullem 10894 resqrexlemover 11033 resqrexlemcalc1 11037 bdtrilem 11261 binomlem 11505 mul4sqlem 12405 dvexp 14528 rpcxpadd 14679 binom4 14750 2sqlem4 14818 |
Copyright terms: Public domain | W3C validator |