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Mirrors > Home > ILE Home > Th. List > r2alf | Unicode version |
Description: Double restricted universal quantification. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
r2alf.1 |
Ref | Expression |
---|---|
r2alf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2353 | . 2 | |
2 | r2alf.1 | . . . . . 6 | |
3 | 2 | nfcri 2213 | . . . . 5 |
4 | 3 | 19.21 1515 | . . . 4 |
5 | impexp 259 | . . . . 5 | |
6 | 5 | albii 1399 | . . . 4 |
7 | df-ral 2353 | . . . . 5 | |
8 | 7 | imbi2i 224 | . . . 4 |
9 | 4, 6, 8 | 3bitr4i 210 | . . 3 |
10 | 9 | albii 1399 | . 2 |
11 | 1, 10 | bitr4i 185 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wcel 1433 wnfc 2206 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-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-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 |
This theorem is referenced by: r2al 2385 ralcomf 2515 |
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