Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 1478. (Contributed by Jim Kingdon, 15-Mar-2018.) |
Ref | Expression |
---|---|
dfexdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alnex 1475 | . . 3 | |
2 | 1 | a1i 9 | . 2 DECID |
3 | 2 | con2biidc 864 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 DECID wdc 819 wal 1329 wex 1468 |
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-gen 1425 ax-ie2 1470 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-tru 1334 df-fal 1337 |
This theorem is referenced by: dfrex2dc 2428 |
Copyright terms: Public domain | W3C validator |