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Mirrors > Home > ILE Home > Th. List > mo3h | Unicode version |
Description: Alternate definition of "at most one." Definition of [BellMachover] p. 460, except that definition has the side condition that not occur in in place of our hypothesis. (Contributed by NM, 8-Mar-1995.) (New usage is discouraged.) |
Ref | Expression |
---|---|
mo3h.1 |
Ref | Expression |
---|---|
mo3h |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mo3h.1 | . . . . . . 7 | |
2 | 1 | nfi 1351 | . . . . . 6 |
3 | 2 | eu2 1944 | . . . . 5 |
4 | 3 | imbi2i 215 | . . . 4 |
5 | df-mo 1904 | . . . 4 | |
6 | anclb 302 | . . . 4 | |
7 | 4, 5, 6 | 3bitr4i 201 | . . 3 |
8 | 19.38 1566 | . . . . 5 | |
9 | 2 | 19.21 1475 | . . . . . 6 |
10 | 9 | albii 1359 | . . . . 5 |
11 | 8, 10 | sylibr 137 | . . . 4 |
12 | anabs5 507 | . . . . . 6 | |
13 | pm3.31 249 | . . . . . 6 | |
14 | 12, 13 | syl5bir 142 | . . . . 5 |
15 | 14 | 2alimi 1345 | . . . 4 |
16 | 11, 15 | syl 14 | . . 3 |
17 | 7, 16 | sylbi 114 | . 2 |
18 | 3 | simplbi2com 1333 | . . 3 |
19 | 18, 5 | sylibr 137 | . 2 |
20 | 17, 19 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wex 1381 wsb 1645 weu 1900 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 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 |
This theorem is referenced by: mo3 1954 mo2dc 1955 mo4f 1960 moim 1964 moimv 1966 moanim 1974 mopick 1978 |
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