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Mirrors > Home > ILE Home > Th. List > sbnf2 | Unicode version |
Description: Two ways of expressing " is (effectively) not free in ." (Contributed by Gérard Lang, 14-Nov-2013.) (Revised by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
sbnf2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2albiim 1377 | . 2 | |
2 | df-nf 1350 | . . . . 5 | |
3 | sbhb 1816 | . . . . . 6 | |
4 | 3 | albii 1359 | . . . . 5 |
5 | alcom 1367 | . . . . 5 | |
6 | 2, 4, 5 | 3bitri 195 | . . . 4 |
7 | nfv 1421 | . . . . . . 7 | |
8 | 7 | sb8 1736 | . . . . . 6 |
9 | nfs1v 1815 | . . . . . . . 8 | |
10 | 9 | sblim 1831 | . . . . . . 7 |
11 | 10 | albii 1359 | . . . . . 6 |
12 | 8, 11 | bitri 173 | . . . . 5 |
13 | 12 | albii 1359 | . . . 4 |
14 | alcom 1367 | . . . 4 | |
15 | 6, 13, 14 | 3bitri 195 | . . 3 |
16 | sbhb 1816 | . . . . . 6 | |
17 | 16 | albii 1359 | . . . . 5 |
18 | alcom 1367 | . . . . 5 | |
19 | 2, 17, 18 | 3bitri 195 | . . . 4 |
20 | nfv 1421 | . . . . . . 7 | |
21 | 20 | sb8 1736 | . . . . . 6 |
22 | nfs1v 1815 | . . . . . . . 8 | |
23 | 22 | sblim 1831 | . . . . . . 7 |
24 | 23 | albii 1359 | . . . . . 6 |
25 | 21, 24 | bitri 173 | . . . . 5 |
26 | 25 | albii 1359 | . . . 4 |
27 | 19, 26 | bitri 173 | . . 3 |
28 | 15, 27 | anbi12i 433 | . 2 |
29 | anidm 376 | . 2 | |
30 | 1, 28, 29 | 3bitr2ri 198 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wnf 1349 wsb 1645 |
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-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 |
This theorem is referenced by: sbnfc2 2906 |
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