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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 3346 | . . 3 |
4 | 3 | pm5.74i 178 | . 2 |
5 | ralm 3345 | . 2 | |
6 | jcab 567 | . . 3 | |
7 | ralm 3345 | . . . 4 | |
8 | eleq1 2141 | . . . . . . 7 | |
9 | 8 | cbvexv 1836 | . . . . . 6 |
10 | 9 | imbi1i 236 | . . . . 5 |
11 | ralm 3345 | . . . . 5 | |
12 | 10, 11 | bitri 182 | . . . 4 |
13 | 7, 12 | anbi12i 447 | . . 3 |
14 | 6, 13 | bitri 182 | . 2 |
15 | 4, 5, 14 | 3bitr3i 208 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wnf 1389 wex 1421 wcel 1433 wral 2348 |
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-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 |
This theorem is referenced by: raaanv 3348 |
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