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Mirrors > Home > ILE Home > Th. List > reu2 | Unicode version |
Description: A way to express restricted uniqueness. (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
reu2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1521 | . . 3 | |
2 | 1 | eu2 2063 | . 2 |
3 | df-reu 2455 | . 2 | |
4 | df-rex 2454 | . . 3 | |
5 | df-ral 2453 | . . . 4 | |
6 | 19.21v 1866 | . . . . . 6 | |
7 | nfv 1521 | . . . . . . . . . . . . 13 | |
8 | nfs1v 1932 | . . . . . . . . . . . . 13 | |
9 | 7, 8 | nfan 1558 | . . . . . . . . . . . 12 |
10 | eleq1 2233 | . . . . . . . . . . . . 13 | |
11 | sbequ12 1764 | . . . . . . . . . . . . 13 | |
12 | 10, 11 | anbi12d 470 | . . . . . . . . . . . 12 |
13 | 9, 12 | sbie 1784 | . . . . . . . . . . 11 |
14 | 13 | anbi2i 454 | . . . . . . . . . 10 |
15 | an4 581 | . . . . . . . . . 10 | |
16 | 14, 15 | bitri 183 | . . . . . . . . 9 |
17 | 16 | imbi1i 237 | . . . . . . . 8 |
18 | impexp 261 | . . . . . . . 8 | |
19 | impexp 261 | . . . . . . . 8 | |
20 | 17, 18, 19 | 3bitri 205 | . . . . . . 7 |
21 | 20 | albii 1463 | . . . . . 6 |
22 | df-ral 2453 | . . . . . . 7 | |
23 | 22 | imbi2i 225 | . . . . . 6 |
24 | 6, 21, 23 | 3bitr4i 211 | . . . . 5 |
25 | 24 | albii 1463 | . . . 4 |
26 | 5, 25 | bitr4i 186 | . . 3 |
27 | 4, 26 | anbi12i 457 | . 2 |
28 | 2, 3, 27 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wex 1485 wsb 1755 weu 2019 wcel 2141 wral 2448 wrex 2449 wreu 2450 |
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-nf 1454 df-sb 1756 df-eu 2022 df-cleq 2163 df-clel 2166 df-ral 2453 df-rex 2454 df-reu 2455 |
This theorem is referenced by: (None) |
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