Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sb8iota | Unicode version |
Description: Variable substitution in description binder. Compare sb8eu 1913. (Contributed by NM, 18-Mar-2013.) |
Ref | Expression |
---|---|
sb8iota.1 |
Ref | Expression |
---|---|
sb8iota |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1421 | . . . . . 6 | |
2 | 1 | sb8 1736 | . . . . 5 |
3 | sbbi 1833 | . . . . . . 7 | |
4 | sb8iota.1 | . . . . . . . . 9 | |
5 | 4 | nfsb 1822 | . . . . . . . 8 |
6 | equsb3 1825 | . . . . . . . . 9 | |
7 | nfv 1421 | . . . . . . . . 9 | |
8 | 6, 7 | nfxfr 1363 | . . . . . . . 8 |
9 | 5, 8 | nfbi 1481 | . . . . . . 7 |
10 | 3, 9 | nfxfr 1363 | . . . . . 6 |
11 | nfv 1421 | . . . . . 6 | |
12 | sbequ 1721 | . . . . . 6 | |
13 | 10, 11, 12 | cbval 1637 | . . . . 5 |
14 | equsb3 1825 | . . . . . . 7 | |
15 | 14 | sblbis 1834 | . . . . . 6 |
16 | 15 | albii 1359 | . . . . 5 |
17 | 2, 13, 16 | 3bitri 195 | . . . 4 |
18 | 17 | abbii 2153 | . . 3 |
19 | 18 | unieqi 3590 | . 2 |
20 | dfiota2 4868 | . 2 | |
21 | dfiota2 4868 | . 2 | |
22 | 19, 20, 21 | 3eqtr4i 2070 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 98 wal 1241 wceq 1243 wnf 1349 wsb 1645 cab 2026 cuni 3580 cio 4865 |
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 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-sn 3381 df-uni 3581 df-iota 4867 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |