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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 2311 | . 2 | |
2 | r2alf.1 | . . . . . 6 | |
3 | 2 | nfcri 2172 | . . . . 5 |
4 | 3 | 19.21 1475 | . . . 4 |
5 | impexp 250 | . . . . 5 | |
6 | 5 | albii 1359 | . . . 4 |
7 | df-ral 2311 | . . . . 5 | |
8 | 7 | imbi2i 215 | . . . 4 |
9 | 4, 6, 8 | 3bitr4i 201 | . . 3 |
10 | 9 | albii 1359 | . 2 |
11 | 1, 10 | bitr4i 176 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wcel 1393 wnfc 2165 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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 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-nf 1350 df-sb 1646 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 |
This theorem is referenced by: r2al 2343 ralcomf 2471 |
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