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Mirrors > Home > ILE Home > Th. List > r3al | Unicode version |
Description: Triple restricted universal quantification. (Contributed by NM, 19-Nov-1995.) |
Ref | Expression |
---|---|
r3al |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2453 | . 2 | |
2 | r2al 2489 | . . 3 | |
3 | 2 | ralbii 2476 | . 2 |
4 | 3anass 977 | . . . . . . . . 9 | |
5 | 4 | imbi1i 237 | . . . . . . . 8 |
6 | impexp 261 | . . . . . . . 8 | |
7 | 5, 6 | bitri 183 | . . . . . . 7 |
8 | 7 | albii 1463 | . . . . . 6 |
9 | 19.21v 1866 | . . . . . 6 | |
10 | 8, 9 | bitri 183 | . . . . 5 |
11 | 10 | albii 1463 | . . . 4 |
12 | 19.21v 1866 | . . . 4 | |
13 | 11, 12 | bitri 183 | . . 3 |
14 | 13 | albii 1463 | . 2 |
15 | 1, 3, 14 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 973 wal 1346 wcel 2141 wral 2448 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 |
This theorem is referenced by: pocl 4288 soss 4299 |
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