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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 2447 | . 2 | |
2 | r2alf.1 | . . . . . 6 | |
3 | 2 | nfcri 2300 | . . . . 5 |
4 | 3 | 19.21 1570 | . . . 4 |
5 | impexp 261 | . . . . 5 | |
6 | 5 | albii 1457 | . . . 4 |
7 | df-ral 2447 | . . . . 5 | |
8 | 7 | imbi2i 225 | . . . 4 |
9 | 4, 6, 8 | 3bitr4i 211 | . . 3 |
10 | 9 | albii 1457 | . 2 |
11 | 1, 10 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wcel 2135 wnfc 2293 wral 2442 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 |
This theorem is referenced by: r2al 2483 ralcomf 2625 |
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