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Mirrors > Home > ILE Home > Th. List > rmo3 | Unicode version |
Description: Restricted "at most one" using explicit substitution. (Contributed by NM, 4-Nov-2012.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
rmo2.1 |
Ref | Expression |
---|---|
rmo3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2356 | . 2 | |
2 | sban 1870 | . . . . . . . . . . 11 | |
3 | clelsb3 2183 | . . . . . . . . . . . 12 | |
4 | 3 | anbi1i 445 | . . . . . . . . . . 11 |
5 | 2, 4 | bitri 182 | . . . . . . . . . 10 |
6 | 5 | anbi2i 444 | . . . . . . . . 9 |
7 | an4 550 | . . . . . . . . 9 | |
8 | ancom 262 | . . . . . . . . . 10 | |
9 | 8 | anbi1i 445 | . . . . . . . . 9 |
10 | 6, 7, 9 | 3bitri 204 | . . . . . . . 8 |
11 | 10 | imbi1i 236 | . . . . . . 7 |
12 | impexp 259 | . . . . . . 7 | |
13 | impexp 259 | . . . . . . 7 | |
14 | 11, 12, 13 | 3bitri 204 | . . . . . 6 |
15 | 14 | albii 1399 | . . . . 5 |
16 | df-ral 2353 | . . . . 5 | |
17 | r19.21v 2438 | . . . . 5 | |
18 | 15, 16, 17 | 3bitr2i 206 | . . . 4 |
19 | 18 | albii 1399 | . . 3 |
20 | nfv 1461 | . . . . 5 | |
21 | rmo2.1 | . . . . 5 | |
22 | 20, 21 | nfan 1497 | . . . 4 |
23 | 22 | mo3 1995 | . . 3 |
24 | df-ral 2353 | . . 3 | |
25 | 19, 23, 24 | 3bitr4i 210 | . 2 |
26 | 1, 25 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wnf 1389 wcel 1433 wsb 1685 wmo 1942 wral 2348 wrmo 2351 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 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-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-cleq 2074 df-clel 2077 df-ral 2353 df-rmo 2356 |
This theorem is referenced by: (None) |
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