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Theorem notnotrd 105
Description: Deduction converting double-negation into the original wff, aka the double negation rule. A translation of natural deduction rule ¬ ¬ -C, Gamma ¬ ¬ ψ => Gamma ψ; 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.)
Hypothesis
Ref Expression
notnotrd.1 (φ → ¬ ¬ ψ)
Assertion
Ref Expression
notnotrd (φψ)

Proof of Theorem notnotrd
StepHypRef Expression
1 notnotrd.1 . 2 (φ → ¬ ¬ ψ)
2 notnot2 104 . 2 (¬ ¬ ψψ)
31, 2syl 15 1 (φψ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem is referenced by:  efald  1334
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