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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 1449 | . . . . . 6 |
3 | 2 | eu2 2057 | . . . . 5 |
4 | 3 | imbi2i 225 | . . . 4 |
5 | df-mo 2017 | . . . 4 | |
6 | anclb 317 | . . . 4 | |
7 | 4, 5, 6 | 3bitr4i 211 | . . 3 |
8 | 19.38 1663 | . . . . 5 | |
9 | 2 | 19.21 1570 | . . . . . 6 |
10 | 9 | albii 1457 | . . . . 5 |
11 | 8, 10 | sylibr 133 | . . . 4 |
12 | anabs5 563 | . . . . . 6 | |
13 | pm3.31 260 | . . . . . 6 | |
14 | 12, 13 | syl5bir 152 | . . . . 5 |
15 | 14 | 2alimi 1443 | . . . 4 |
16 | 11, 15 | syl 14 | . . 3 |
17 | 7, 16 | sylbi 120 | . 2 |
18 | 3 | simplbi2com 1431 | . . 3 |
19 | 18, 5 | sylibr 133 | . 2 |
20 | 17, 19 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wex 1479 wsb 1749 weu 2013 wmo 2014 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 |
This theorem is referenced by: mo3 2067 mo2dc 2068 mo4f 2073 moim 2077 moimv 2079 moanim 2087 mopick 2091 |
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