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Mirrors > Home > ILE Home > Th. List > rmob | Unicode version |
Description: Consequence of "at most one", using implicit substitution. (Contributed by NM, 2-Jan-2015.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
rmoi.b | |
rmoi.c |
Ref | Expression |
---|---|
rmob |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2314 | . 2 | |
2 | simprl 483 | . . . 4 | |
3 | eleq1 2100 | . . . 4 | |
4 | 2, 3 | syl5ibcom 144 | . . 3 |
5 | simpl 102 | . . . 4 | |
6 | 5 | a1i 9 | . . 3 |
7 | simplrl 487 | . . . . 5 | |
8 | simpr 103 | . . . . 5 | |
9 | simpll 481 | . . . . 5 | |
10 | simplrr 488 | . . . . 5 | |
11 | eleq1 2100 | . . . . . . 7 | |
12 | rmoi.b | . . . . . . 7 | |
13 | 11, 12 | anbi12d 442 | . . . . . 6 |
14 | eleq1 2100 | . . . . . . 7 | |
15 | rmoi.c | . . . . . . 7 | |
16 | 14, 15 | anbi12d 442 | . . . . . 6 |
17 | 13, 16 | mob 2723 | . . . . 5 |
18 | 7, 8, 9, 7, 10, 17 | syl212anc 1145 | . . . 4 |
19 | 18 | ex 108 | . . 3 |
20 | 4, 6, 19 | pm5.21ndd 621 | . 2 |
21 | 1, 20 | sylanb 268 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 wmo 1901 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-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rmo 2314 df-v 2559 |
This theorem is referenced by: rmoi 2851 |
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