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Mirrors > Home > ILE Home > Th. List > reu3 | Unicode version |
Description: A way to express restricted uniqueness. (Contributed by NM, 24-Oct-2006.) |
Ref | Expression |
---|---|
reu3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reurex 2621 | . . 3 | |
2 | reu6 2846 | . . . 4 | |
3 | bi1 117 | . . . . . 6 | |
4 | 3 | ralimi 2472 | . . . . 5 |
5 | 4 | reximi 2506 | . . . 4 |
6 | 2, 5 | sylbi 120 | . . 3 |
7 | 1, 6 | jca 304 | . 2 |
8 | rexex 2456 | . . . 4 | |
9 | 8 | anim2i 339 | . . 3 |
10 | nfv 1493 | . . . . 5 | |
11 | 10 | eu3 2023 | . . . 4 |
12 | df-reu 2400 | . . . 4 | |
13 | df-rex 2399 | . . . . 5 | |
14 | df-ral 2398 | . . . . . . 7 | |
15 | impexp 261 | . . . . . . . 8 | |
16 | 15 | albii 1431 | . . . . . . 7 |
17 | 14, 16 | bitr4i 186 | . . . . . 6 |
18 | 17 | exbii 1569 | . . . . 5 |
19 | 13, 18 | anbi12i 455 | . . . 4 |
20 | 11, 12, 19 | 3bitr4i 211 | . . 3 |
21 | 9, 20 | sylibr 133 | . 2 |
22 | 7, 21 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wex 1453 wcel 1465 weu 1977 wral 2393 wrex 2394 wreu 2395 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-cleq 2110 df-clel 2113 df-ral 2398 df-rex 2399 df-reu 2400 df-rmo 2401 |
This theorem is referenced by: reu7 2852 bdreu 12980 |
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