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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 559, holds for all propositions, not just decidable ones. (Contributed by Jim Kingdon, 13-Mar-2018.) |
Ref | Expression |
---|---|
notnotbdc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 559 | . 2 | |
2 | notnotrdc 751 | . 2 DECID | |
3 | 1, 2 | impbid2 131 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 98 DECID wdc 742 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 |
This theorem depends on definitions: df-bi 110 df-dc 743 |
This theorem is referenced by: con1biidc 771 imandc 786 imordc 796 dfbi3dc 1288 alexdc 1510 |
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