Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > raaan | Unicode version |
Description: Rearrange restricted quantifiers. (Contributed by NM, 26-Oct-2010.) |
Ref | Expression |
---|---|
raaan.1 | |
raaan.2 |
Ref | Expression |
---|---|
raaan |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raaan.1 | . . . 4 | |
2 | raaan.2 | . . . 4 | |
3 | 1, 2 | raaanlem 3326 | . . 3 |
4 | 3 | pm5.74i 169 | . 2 |
5 | ralm 3325 | . 2 | |
6 | jcab 535 | . . 3 | |
7 | ralm 3325 | . . . 4 | |
8 | eleq1 2100 | . . . . . . 7 | |
9 | 8 | cbvexv 1795 | . . . . . 6 |
10 | 9 | imbi1i 227 | . . . . 5 |
11 | ralm 3325 | . . . . 5 | |
12 | 10, 11 | bitri 173 | . . . 4 |
13 | 7, 12 | anbi12i 433 | . . 3 |
14 | 6, 13 | bitri 173 | . 2 |
15 | 4, 5, 14 | 3bitr3i 199 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wnf 1349 wex 1381 wcel 1393 wral 2306 |
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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 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-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 |
This theorem is referenced by: raaanv 3328 |
Copyright terms: Public domain | W3C validator |