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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 2356 | . 2 | |
2 | simprl 497 | . . . 4 | |
3 | eleq1 2141 | . . . 4 | |
4 | 2, 3 | syl5ibcom 153 | . . 3 |
5 | simpl 107 | . . . 4 | |
6 | 5 | a1i 9 | . . 3 |
7 | simplrl 501 | . . . . 5 | |
8 | simpr 108 | . . . . 5 | |
9 | simpll 495 | . . . . 5 | |
10 | simplrr 502 | . . . . 5 | |
11 | eleq1 2141 | . . . . . . 7 | |
12 | rmoi.b | . . . . . . 7 | |
13 | 11, 12 | anbi12d 456 | . . . . . 6 |
14 | eleq1 2141 | . . . . . . 7 | |
15 | rmoi.c | . . . . . . 7 | |
16 | 14, 15 | anbi12d 456 | . . . . . 6 |
17 | 13, 16 | mob 2774 | . . . . 5 |
18 | 7, 8, 9, 7, 10, 17 | syl212anc 1179 | . . . 4 |
19 | 18 | ex 113 | . . 3 |
20 | 4, 6, 19 | pm5.21ndd 653 | . 2 |
21 | 1, 20 | sylanb 278 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wcel 1433 wmo 1942 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-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rmo 2356 df-v 2603 |
This theorem is referenced by: rmoi 2907 |
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