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Mirrors > Home > ILE Home > Th. List > sb8eu | Unicode version |
Description: Variable substitution in uniqueness quantifier. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
sb8eu.1 |
Ref | Expression |
---|---|
sb8eu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1461 | . . . . 5 | |
2 | 1 | sb8 1777 | . . . 4 |
3 | sbbi 1874 | . . . . . 6 | |
4 | sb8eu.1 | . . . . . . . 8 | |
5 | 4 | nfsb 1863 | . . . . . . 7 |
6 | equsb3 1866 | . . . . . . . 8 | |
7 | nfv 1461 | . . . . . . . 8 | |
8 | 6, 7 | nfxfr 1403 | . . . . . . 7 |
9 | 5, 8 | nfbi 1521 | . . . . . 6 |
10 | 3, 9 | nfxfr 1403 | . . . . 5 |
11 | nfv 1461 | . . . . 5 | |
12 | sbequ 1761 | . . . . 5 | |
13 | 10, 11, 12 | cbval 1677 | . . . 4 |
14 | equsb3 1866 | . . . . . 6 | |
15 | 14 | sblbis 1875 | . . . . 5 |
16 | 15 | albii 1399 | . . . 4 |
17 | 2, 13, 16 | 3bitri 204 | . . 3 |
18 | 17 | exbii 1536 | . 2 |
19 | df-eu 1944 | . 2 | |
20 | df-eu 1944 | . 2 | |
21 | 18, 19, 20 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 103 wal 1282 wnf 1389 wex 1421 wsb 1685 weu 1941 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 |
This theorem is referenced by: sb8mo 1955 nfeud 1957 nfeu 1960 cbveu 1965 cbvreu 2575 acexmid 5531 |
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