Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > difundi | Unicode version |
Description: Distributive law for class difference. Theorem 39 of [Suppes] p. 29. (Contributed by NM, 17-Aug-2004.) |
Ref | Expression |
---|---|
difundi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 2927 | . . . 4 | |
2 | eldif 2927 | . . . 4 | |
3 | 1, 2 | anbi12i 433 | . . 3 |
4 | elin 3126 | . . 3 | |
5 | eldif 2927 | . . . . . 6 | |
6 | elun 3084 | . . . . . . . 8 | |
7 | 6 | notbii 594 | . . . . . . 7 |
8 | 7 | anbi2i 430 | . . . . . 6 |
9 | 5, 8 | bitri 173 | . . . . 5 |
10 | ioran 669 | . . . . . 6 | |
11 | 10 | anbi2i 430 | . . . . 5 |
12 | 9, 11 | bitri 173 | . . . 4 |
13 | anandi 524 | . . . 4 | |
14 | 12, 13 | bitri 173 | . . 3 |
15 | 3, 4, 14 | 3bitr4ri 202 | . 2 |
16 | 15 | eqriv 2037 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 97 wo 629 wceq 1243 wcel 1393 cdif 2914 cun 2915 cin 2916 |
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-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 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-nfc 2167 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 |
This theorem is referenced by: undm 3195 |
Copyright terms: Public domain | W3C validator |