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Mirrors > Home > ILE Home > Th. List > peircedc | Unicode version |
Description: Peirce's theorem for a decidable proposition. This odd-looking theorem can be seen as an alternative to exmiddc 822, condc 839, or notnotrdc 829 in the sense of expressing the "difference" between an intuitionistic system of propositional calculus and a classical system. In intuitionistic logic, it only holds for decidable propositions. (Contributed by Jim Kingdon, 3-Jul-2018.) |
Ref | Expression |
---|---|
peircedc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 821 | . 2 DECID | |
2 | ax-1 6 | . . 3 | |
3 | pm2.21 607 | . . . . 5 | |
4 | 3 | imim1i 60 | . . . 4 |
5 | 4 | com12 30 | . . 3 |
6 | 2, 5 | jaoi 706 | . 2 |
7 | 1, 6 | sylbi 120 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wo 698 DECID wdc 820 |
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-in2 605 ax-io 699 |
This theorem depends on definitions: df-bi 116 df-dc 821 |
This theorem is referenced by: looinvdc 901 exmoeudc 2069 |
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