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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 2040 | . 2 |
3 | exmiddc 821 | . . 3 DECID | |
4 | 1 | mor 2041 | . . . 4 |
5 | 1 | mo2n 2027 | . . . . 5 |
6 | 5 | a1d 22 | . . . 4 |
7 | 4, 6 | jaoi 705 | . . 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 697 DECID wdc 819 wal 1329 wnf 1436 wex 1468 wsb 1735 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 |
This theorem is referenced by: mo2dc 2054 |
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