Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 1521 | . . . . 5 | |
2 | 1 | sb8 1849 | . . . 4 |
3 | sbbi 1952 | . . . . . 6 | |
4 | sb8eu.1 | . . . . . . . 8 | |
5 | 4 | nfsb 1939 | . . . . . . 7 |
6 | equsb3 1944 | . . . . . . . 8 | |
7 | nfv 1521 | . . . . . . . 8 | |
8 | 6, 7 | nfxfr 1467 | . . . . . . 7 |
9 | 5, 8 | nfbi 1582 | . . . . . 6 |
10 | 3, 9 | nfxfr 1467 | . . . . 5 |
11 | nfv 1521 | . . . . 5 | |
12 | sbequ 1833 | . . . . 5 | |
13 | 10, 11, 12 | cbval 1747 | . . . 4 |
14 | equsb3 1944 | . . . . . 6 | |
15 | 14 | sblbis 1953 | . . . . 5 |
16 | 15 | albii 1463 | . . . 4 |
17 | 2, 13, 16 | 3bitri 205 | . . 3 |
18 | 17 | exbii 1598 | . 2 |
19 | df-eu 2022 | . 2 | |
20 | df-eu 2022 | . 2 | |
21 | 18, 19, 20 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1346 wnf 1453 wex 1485 wsb 1755 weu 2019 |
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 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 |
This theorem is referenced by: sb8mo 2033 nfeud 2035 nfeu 2038 cbveu 2043 cbvreu 2694 acexmid 5849 |
Copyright terms: Public domain | W3C validator |