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Mirrors > Home > ILE Home > Th. List > modc | Unicode version |
Description: Equivalent definitions of "there exists at most one," given decidable existence. (Contributed by Jim Kingdon, 1-Jul-2018.) |
Ref | Expression |
---|---|
modc.1 |
Ref | Expression |
---|---|
modc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | modc.1 | . . 3 | |
2 | 1 | mo23 2054 | . 2 |
3 | exmiddc 826 | . . 3 DECID | |
4 | 1 | mor 2055 | . . . 4 |
5 | 1 | mo2n 2041 | . . . . 5 |
6 | 5 | a1d 22 | . . . 4 |
7 | 4, 6 | jaoi 706 | . . 3 |
8 | 3, 7 | syl 14 | . 2 DECID |
9 | 2, 8 | impbid2 142 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 698 DECID wdc 824 wal 1340 wnf 1447 wex 1479 wsb 1749 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 |
This theorem depends on definitions: df-bi 116 df-dc 825 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 |
This theorem is referenced by: mo2dc 2068 |
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