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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 782, condc 787, or notnotrdc 789 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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 781 |
. 2
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2 | ax-1 5 |
. . 3
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3 | pm2.21 582 |
. . . . 5
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4 | 3 | imim1i 59 |
. . . 4
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5 | 4 | com12 30 |
. . 3
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6 | 2, 5 | jaoi 671 |
. 2
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7 | 1, 6 | sylbi 119 |
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 104 ax-ia2 105 ax-ia3 106 ax-in2 580 ax-io 665 |
This theorem depends on definitions: df-bi 115 df-dc 781 |
This theorem is referenced by: looinvdc 859 exmoeudc 2011 |
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