Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dvds0lem | Unicode version |
Description: A lemma to assist theorems of with no antecedents. (Contributed by Paul Chapman, 21-Mar-2011.) |
Ref | Expression |
---|---|
dvds0lem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1 5539 | . . . . . . . . 9 | |
2 | 1 | eqeq1d 2089 | . . . . . . . 8 |
3 | 2 | rspcev 2701 | . . . . . . 7 |
4 | 3 | adantl 271 | . . . . . 6 |
5 | divides 10197 | . . . . . . 7 | |
6 | 5 | adantr 270 | . . . . . 6 |
7 | 4, 6 | mpbird 165 | . . . . 5 |
8 | 7 | expr 367 | . . . 4 |
9 | 8 | 3impa 1133 | . . 3 |
10 | 9 | 3comr 1146 | . 2 |
11 | 10 | imp 122 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wceq 1284 wcel 1433 wrex 2349 class class class wbr 3785 (class class class)co 5532 cmul 6986 cz 8351 cdvds 10195 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-iota 4887 df-fv 4930 df-ov 5535 df-dvds 10196 |
This theorem is referenced by: iddvds 10208 1dvds 10209 dvds0 10210 dvdsmul1 10217 dvdsmul2 10218 divalgmod 10327 oddpwdclemxy 10547 ex-dvds 10567 |
Copyright terms: Public domain | W3C validator |