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Mirrors > Home > ILE Home > Th. List > dfexdc | Unicode version |
Description: Defining given decidability. It is common in classical logic to define as but in intuitionistic logic without a decidability condition, that is only an implication not an equivalence, as seen at exalim 1431. (Contributed by Jim Kingdon, 15-Mar-2018.) |
Ref | Expression |
---|---|
dfexdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alnex 1428 | . . 3 | |
2 | 1 | a1i 9 | . 2 DECID |
3 | 2 | con2biidc 806 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 103 DECID wdc 775 wal 1282 wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-gen 1378 ax-ie2 1423 |
This theorem depends on definitions: df-bi 115 df-dc 776 df-tru 1287 df-fal 1290 |
This theorem is referenced by: (None) |
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