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Mirrors > Home > ILE Home > Th. List > raaanlem | Unicode version |
Description: Special case of raaan 3347 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 2141 | . . . 4 | |
2 | 1 | cbvexv 1836 | . . 3 |
3 | raaan.1 | . . . . 5 | |
4 | 3 | r19.28m 3331 | . . . 4 |
5 | 4 | ralbidv 2368 | . . 3 |
6 | 2, 5 | sylbi 119 | . 2 |
7 | nfcv 2219 | . . . 4 | |
8 | raaan.2 | . . . 4 | |
9 | 7, 8 | nfralxy 2402 | . . 3 |
10 | 9 | r19.27m 3336 | . 2 |
11 | 6, 10 | bitrd 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wnf 1389 wex 1421 wcel 1433 wral 2348 |
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-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 |
This theorem is referenced by: raaan 3347 |
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