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Mirrors > Home > ILE Home > Th. List > raaanlem | Unicode version |
Description: Special case of raaan 3464 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 2200 | . . . 4 | |
2 | 1 | cbvexv 1890 | . . 3 |
3 | raaan.1 | . . . . 5 | |
4 | 3 | r19.28m 3447 | . . . 4 |
5 | 4 | ralbidv 2435 | . . 3 |
6 | 2, 5 | sylbi 120 | . 2 |
7 | nfcv 2279 | . . . 4 | |
8 | raaan.2 | . . . 4 | |
9 | 7, 8 | nfralxy 2469 | . . 3 |
10 | 9 | r19.27m 3453 | . 2 |
11 | 6, 10 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wnf 1436 wex 1468 wcel 1480 wral 2414 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 |
This theorem is referenced by: raaan 3464 |
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