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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 |
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Ref | Expression |
---|---|
modc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | modc.1 |
. . 3
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2 | 1 | mo23 1938 |
. 2
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3 | exmiddc 743 |
. . 3
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4 | 1 | mor 1939 |
. . . 4
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5 | 1 | mo2n 1925 |
. . . . 5
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6 | 5 | a1d 22 |
. . . 4
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7 | 4, 6 | jaoi 635 |
. . 3
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8 | 3, 7 | syl 14 |
. 2
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9 | 2, 8 | impbid2 131 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-in1 544 ax-in2 545 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-dc 742 df-tru 1245 df-fal 1248 df-nf 1347 df-sb 1643 |
This theorem is referenced by: mo2dc 1952 |
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