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Mirrors > Home > ILE Home > Th. List > raaanlem | Unicode version |
Description: Special case of raaan 3327 where is inhabited. (Contributed by Jim Kingdon, 6-Aug-2018.) |
Ref | Expression |
---|---|
raaan.1 | |
raaan.2 |
Ref | Expression |
---|---|
raaanlem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2100 | . . . 4 | |
2 | 1 | cbvexv 1795 | . . 3 |
3 | raaan.1 | . . . . 5 | |
4 | 3 | r19.28m 3311 | . . . 4 |
5 | 4 | ralbidv 2326 | . . 3 |
6 | 2, 5 | sylbi 114 | . 2 |
7 | nfcv 2178 | . . . 4 | |
8 | raaan.2 | . . . 4 | |
9 | 7, 8 | nfralxy 2360 | . . 3 |
10 | 9 | r19.27m 3316 | . 2 |
11 | 6, 10 | bitrd 177 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wnf 1349 wex 1381 wcel 1393 wral 2306 |
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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 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-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 |
This theorem is referenced by: raaan 3327 |
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