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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 1460 | . . . . . 6 |
3 | 2 | eu2 2068 | . . . . 5 |
4 | 3 | imbi2i 226 | . . . 4 |
5 | df-mo 2028 | . . . 4 | |
6 | anclb 319 | . . . 4 | |
7 | 4, 5, 6 | 3bitr4i 212 | . . 3 |
8 | 19.38 1674 | . . . . 5 | |
9 | 2 | 19.21 1581 | . . . . . 6 |
10 | 9 | albii 1468 | . . . . 5 |
11 | 8, 10 | sylibr 134 | . . . 4 |
12 | anabs5 573 | . . . . . 6 | |
13 | pm3.31 262 | . . . . . 6 | |
14 | 12, 13 | syl5bir 153 | . . . . 5 |
15 | 14 | 2alimi 1454 | . . . 4 |
16 | 11, 15 | syl 14 | . . 3 |
17 | 7, 16 | sylbi 121 | . 2 |
18 | 3 | simplbi2com 1442 | . . 3 |
19 | 18, 5 | sylibr 134 | . 2 |
20 | 17, 19 | impbii 126 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 104 wb 105 wal 1351 wex 1490 wsb 1760 weu 2024 wmo 2025 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 |
This theorem depends on definitions: df-bi 117 df-nf 1459 df-sb 1761 df-eu 2027 df-mo 2028 |
This theorem is referenced by: mo3 2078 mo2dc 2079 mo4f 2084 moim 2088 moimv 2090 moanim 2098 mopick 2102 |
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