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Mirrors > Home > ILE Home > Th. List > sb8euh | Unicode version |
Description: Variable substitution in uniqueness quantifier. (Contributed by NM, 7-Aug-1994.) (Revised by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
sb8euh.1 |
Ref | Expression |
---|---|
sb8euh |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1419 | . . . . 5 | |
2 | 1 | sb8h 1734 | . . . 4 |
3 | sbbi 1833 | . . . . . 6 | |
4 | sb8euh.1 | . . . . . . . 8 | |
5 | 4 | hbsb 1823 | . . . . . . 7 |
6 | equsb3 1825 | . . . . . . . 8 | |
7 | ax-17 1419 | . . . . . . . 8 | |
8 | 6, 7 | hbxfrbi 1361 | . . . . . . 7 |
9 | 5, 8 | hbbi 1440 | . . . . . 6 |
10 | 3, 9 | hbxfrbi 1361 | . . . . 5 |
11 | ax-17 1419 | . . . . 5 | |
12 | sbequ 1721 | . . . . 5 | |
13 | 10, 11, 12 | cbvalh 1636 | . . . 4 |
14 | equsb3 1825 | . . . . . 6 | |
15 | 14 | sblbis 1834 | . . . . 5 |
16 | 15 | albii 1359 | . . . 4 |
17 | 2, 13, 16 | 3bitri 195 | . . 3 |
18 | 17 | exbii 1496 | . 2 |
19 | df-eu 1903 | . 2 | |
20 | df-eu 1903 | . 2 | |
21 | 18, 19, 20 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wex 1381 wsb 1645 weu 1900 |
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 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 |
This theorem is referenced by: eu1 1925 |
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