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Mirrors > Home > ILE Home > Th. List > sb8eu | Unicode version |
Description: Variable substitution in unique existential 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 1508 | . . . . 5 | |
2 | 1 | sb8 1828 | . . . 4 |
3 | sbbi 1930 | . . . . . 6 | |
4 | sb8eu.1 | . . . . . . . 8 | |
5 | 4 | nfsb 1917 | . . . . . . 7 |
6 | equsb3 1922 | . . . . . . . 8 | |
7 | nfv 1508 | . . . . . . . 8 | |
8 | 6, 7 | nfxfr 1450 | . . . . . . 7 |
9 | 5, 8 | nfbi 1568 | . . . . . 6 |
10 | 3, 9 | nfxfr 1450 | . . . . 5 |
11 | nfv 1508 | . . . . 5 | |
12 | sbequ 1812 | . . . . 5 | |
13 | 10, 11, 12 | cbval 1727 | . . . 4 |
14 | equsb3 1922 | . . . . . 6 | |
15 | 14 | sblbis 1931 | . . . . 5 |
16 | 15 | albii 1446 | . . . 4 |
17 | 2, 13, 16 | 3bitri 205 | . . 3 |
18 | 17 | exbii 1584 | . 2 |
19 | df-eu 2000 | . 2 | |
20 | df-eu 2000 | . 2 | |
21 | 18, 19, 20 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1329 wnf 1436 wex 1468 wsb 1735 weu 1997 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 |
This theorem is referenced by: sb8mo 2011 nfeud 2013 nfeu 2016 cbveu 2021 cbvreu 2650 acexmid 5766 |
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