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Mirrors > Home > ILE Home > Th. List > rmo3f | Unicode version |
Description: Restricted "at most one" using explicit substitution. (Contributed by NM, 4-Nov-2012.) (Revised by NM, 16-Jun-2017.) (Revised by Thierry Arnoux, 8-Oct-2017.) |
Ref | Expression |
---|---|
rmo3f.1 | |
rmo3f.2 | |
rmo3f.3 |
Ref | Expression |
---|---|
rmo3f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2401 | . 2 | |
2 | sban 1906 | . . . . . . . . . . 11 | |
3 | rmo3f.1 | . . . . . . . . . . . . 13 | |
4 | 3 | clelsb3f 2262 | . . . . . . . . . . . 12 |
5 | 4 | anbi1i 453 | . . . . . . . . . . 11 |
6 | 2, 5 | bitri 183 | . . . . . . . . . 10 |
7 | 6 | anbi2i 452 | . . . . . . . . 9 |
8 | an4 560 | . . . . . . . . 9 | |
9 | ancom 264 | . . . . . . . . . 10 | |
10 | 9 | anbi1i 453 | . . . . . . . . 9 |
11 | 7, 8, 10 | 3bitri 205 | . . . . . . . 8 |
12 | 11 | imbi1i 237 | . . . . . . 7 |
13 | impexp 261 | . . . . . . 7 | |
14 | impexp 261 | . . . . . . 7 | |
15 | 12, 13, 14 | 3bitri 205 | . . . . . 6 |
16 | 15 | albii 1431 | . . . . 5 |
17 | df-ral 2398 | . . . . 5 | |
18 | rmo3f.2 | . . . . . . 7 | |
19 | 18 | nfcri 2252 | . . . . . 6 |
20 | 19 | r19.21 2485 | . . . . 5 |
21 | 16, 17, 20 | 3bitr2i 207 | . . . 4 |
22 | 21 | albii 1431 | . . 3 |
23 | rmo3f.3 | . . . . 5 | |
24 | 19, 23 | nfan 1529 | . . . 4 |
25 | 24 | mo3 2031 | . . 3 |
26 | df-ral 2398 | . . 3 | |
27 | 22, 25, 26 | 3bitr4i 211 | . 2 |
28 | 1, 27 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wnf 1421 wcel 1465 wsb 1720 wmo 1978 wnfc 2245 wral 2393 wrmo 2396 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rmo 2401 |
This theorem is referenced by: rmo4f 2855 |
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