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Mirrors > Home > ILE Home > Th. List > notnotbdc | Unicode version |
Description: Double negation equivalence for a decidable proposition. Like Theorem *4.13 of [WhiteheadRussell] p. 117, but with a decidability antecendent. The forward direction, notnot 594, holds for all propositions, not just decidable ones. (Contributed by Jim Kingdon, 13-Mar-2018.) |
Ref | Expression |
---|---|
notnotbdc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 594 |
. 2
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2 | notnotrdc 789 |
. 2
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3 | 1, 2 | impbid2 141 |
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-in1 579 ax-in2 580 ax-io 665 |
This theorem depends on definitions: df-bi 115 df-dc 781 |
This theorem is referenced by: con1biidc 809 imandc 824 imordc 834 dfbi3dc 1333 alexdc 1555 |
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