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Mirrors > Home > NFE Home > Th. List > notnotrd | Unicode version |
Description: Deduction converting double-negation into the original wff, aka the double negation rule. A translation of natural deduction rule -C, Gamma => Gamma ; see natded in set.mm. This is definition NNC in [Pfenning] p. 17. This rule is valid in classical logic (which MPE uses), but not intuitionistic logic. (Contributed by DAW, 8-Feb-2017.) |
Ref | Expression |
---|---|
notnotrd.1 |
Ref | Expression |
---|---|
notnotrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnotrd.1 | . 2 | |
2 | notnot2 104 | . 2 | |
3 | 1, 2 | syl 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: efald 1334 |
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