Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > opelopabt | Unicode version |
Description: Closed theorem form of opelopab 4026. (Contributed by NM, 19-Feb-2013.) |
Ref | Expression |
---|---|
opelopabt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elopab 4013 | . 2 | |
2 | 19.26-2 1411 | . . . . 5 | |
3 | prth 336 | . . . . . . 7 | |
4 | bitr 455 | . . . . . . 7 | |
5 | 3, 4 | syl6 33 | . . . . . 6 |
6 | 5 | 2alimi 1385 | . . . . 5 |
7 | 2, 6 | sylbir 133 | . . . 4 |
8 | copsex2t 4000 | . . . 4 | |
9 | 7, 8 | sylan 277 | . . 3 |
10 | 9 | 3impa 1133 | . 2 |
11 | 1, 10 | syl5bb 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wal 1282 wceq 1284 wex 1421 wcel 1433 cop 3401 copab 3838 |
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-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-opab 3840 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |