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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 2443 | . 2 | |
2 | sban 1935 | . . . . . . . . . . 11 | |
3 | rmo3f.1 | . . . . . . . . . . . . 13 | |
4 | 3 | clelsb3f 2303 | . . . . . . . . . . . 12 |
5 | 4 | anbi1i 454 | . . . . . . . . . . 11 |
6 | 2, 5 | bitri 183 | . . . . . . . . . 10 |
7 | 6 | anbi2i 453 | . . . . . . . . 9 |
8 | an4 576 | . . . . . . . . 9 | |
9 | ancom 264 | . . . . . . . . . 10 | |
10 | 9 | anbi1i 454 | . . . . . . . . 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 1450 | . . . . 5 |
17 | df-ral 2440 | . . . . 5 | |
18 | rmo3f.2 | . . . . . . 7 | |
19 | 18 | nfcri 2293 | . . . . . 6 |
20 | 19 | r19.21 2533 | . . . . 5 |
21 | 16, 17, 20 | 3bitr2i 207 | . . . 4 |
22 | 21 | albii 1450 | . . 3 |
23 | rmo3f.3 | . . . . 5 | |
24 | 19, 23 | nfan 1545 | . . . 4 |
25 | 24 | mo3 2060 | . . 3 |
26 | df-ral 2440 | . . 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 1333 wnf 1440 wsb 1742 wmo 2007 wcel 2128 wnfc 2286 wral 2435 wrmo 2438 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rmo 2443 |
This theorem is referenced by: rmo4f 2910 |
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