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Mirrors > Home > ILE Home > Th. List > rmo4 | Unicode version |
Description: Restricted "at most one" using implicit substitution. (Contributed by NM, 24-Oct-2006.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
rmo4.1 |
Ref | Expression |
---|---|
rmo4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2314 | . 2 | |
2 | an4 520 | . . . . . . . . 9 | |
3 | ancom 253 | . . . . . . . . . 10 | |
4 | 3 | anbi1i 431 | . . . . . . . . 9 |
5 | 2, 4 | bitri 173 | . . . . . . . 8 |
6 | 5 | imbi1i 227 | . . . . . . 7 |
7 | impexp 250 | . . . . . . 7 | |
8 | impexp 250 | . . . . . . 7 | |
9 | 6, 7, 8 | 3bitri 195 | . . . . . 6 |
10 | 9 | albii 1359 | . . . . 5 |
11 | df-ral 2311 | . . . . 5 | |
12 | r19.21v 2396 | . . . . 5 | |
13 | 10, 11, 12 | 3bitr2i 197 | . . . 4 |
14 | 13 | albii 1359 | . . 3 |
15 | eleq1 2100 | . . . . 5 | |
16 | rmo4.1 | . . . . 5 | |
17 | 15, 16 | anbi12d 442 | . . . 4 |
18 | 17 | mo4 1961 | . . 3 |
19 | df-ral 2311 | . . 3 | |
20 | 14, 18, 19 | 3bitr4i 201 | . 2 |
21 | 1, 20 | bitri 173 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wcel 1393 wmo 1901 wral 2306 wrmo 2309 |
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-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-cleq 2033 df-clel 2036 df-ral 2311 df-rmo 2314 |
This theorem is referenced by: reu4 2735 lteupri 6715 elrealeu 6906 rereceu 6963 qbtwnz 9106 rsqrmo 9625 |
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