Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > disj3 | Unicode version |
Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 19-May-1998.) |
Ref | Expression |
---|---|
disj3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.71 369 | . . . 4 | |
2 | eldif 2927 | . . . . 5 | |
3 | 2 | bibi2i 216 | . . . 4 |
4 | 1, 3 | bitr4i 176 | . . 3 |
5 | 4 | albii 1359 | . 2 |
6 | disj1 3270 | . 2 | |
7 | dfcleq 2034 | . 2 | |
8 | 5, 6, 7 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 wal 1241 wceq 1243 wcel 1393 cdif 2914 cin 2916 c0 3224 |
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-ral 2311 df-v 2559 df-dif 2920 df-in 2924 df-nul 3225 |
This theorem is referenced by: disjel 3274 disj4im 3276 uneqdifeqim 3308 difprsn1 3503 diftpsn3 3505 orddif 4271 phpm 6327 |
Copyright terms: Public domain | W3C validator |