Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > eltpg | Unicode version |
Description: Members of an unordered triple of classes. (Contributed by FL, 2-Feb-2014.) (Proof shortened by Mario Carneiro, 11-Feb-2015.) |
Ref | Expression |
---|---|
eltpg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elprg 3395 | . . 3 | |
2 | elsng 3390 | . . 3 | |
3 | 1, 2 | orbi12d 707 | . 2 |
4 | df-tp 3383 | . . . 4 | |
5 | 4 | eleq2i 2104 | . . 3 |
6 | elun 3084 | . . 3 | |
7 | 5, 6 | bitri 173 | . 2 |
8 | df-3or 886 | . 2 | |
9 | 3, 7, 8 | 3bitr4g 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wo 629 w3o 884 wceq 1243 wcel 1393 cun 2915 csn 3375 cpr 3376 ctp 3377 |
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-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-3or 886 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-un 2922 df-sn 3381 df-pr 3382 df-tp 3383 |
This theorem is referenced by: eltpi 3417 eltp 3418 |
Copyright terms: Public domain | W3C validator |