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Mirrors > Home > ILE Home > Th. List > notnotrdc | Unicode version |
Description: Double negation elimination for a decidable proposition. The converse, notnot 630, holds for all propositions, not just decidable ones. This is Theorem *2.14 of [WhiteheadRussell] p. 102, but with a decidability condition added. (Contributed by Jim Kingdon, 11-Mar-2018.) |
Ref | Expression |
---|---|
notnotrdc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 836 |
. . 3
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2 | orcom 729 |
. . 3
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3 | 1, 2 | bitri 184 |
. 2
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4 | pm2.53 723 |
. 2
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5 | 3, 4 | sylbi 121 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in2 616 ax-io 710 |
This theorem depends on definitions: df-bi 117 df-dc 836 |
This theorem is referenced by: dcstab 845 notnotbdc 873 condandc 882 pm2.13dc 886 pm2.54dc 892 mkvprop 7169 netap 7266 |
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