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Mirrors > Home > ILE Home > Th. List > mob2 | Unicode version |
Description: Consequence of "at most one." (Contributed by NM, 2-Jan-2015.) |
Ref | Expression |
---|---|
moi2.1 |
Ref | Expression |
---|---|
mob2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3 906 | . . 3 | |
2 | moi2.1 | . . 3 | |
3 | 1, 2 | syl5ibcom 144 | . 2 |
4 | nfs1v 1815 | . . . . . . . 8 | |
5 | sbequ12 1654 | . . . . . . . 8 | |
6 | 4, 5 | mo4f 1960 | . . . . . . 7 |
7 | sp 1401 | . . . . . . 7 | |
8 | 6, 7 | sylbi 114 | . . . . . 6 |
9 | nfv 1421 | . . . . . . . . . 10 | |
10 | 9, 2 | sbhypf 2603 | . . . . . . . . 9 |
11 | 10 | anbi2d 437 | . . . . . . . 8 |
12 | eqeq2 2049 | . . . . . . . 8 | |
13 | 11, 12 | imbi12d 223 | . . . . . . 7 |
14 | 13 | spcgv 2640 | . . . . . 6 |
15 | 8, 14 | syl5 28 | . . . . 5 |
16 | 15 | imp 115 | . . . 4 |
17 | 16 | expd 245 | . . 3 |
18 | 17 | 3impia 1101 | . 2 |
19 | 3, 18 | impbid 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wal 1241 wceq 1243 wcel 1393 wsb 1645 wmo 1901 |
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-v 2559 |
This theorem is referenced by: moi2 2722 mob 2723 |
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