Theorem notnotrd

Description: Deduction associated with notnotr and notnotri . Double negation elimination rule. A translation of the natural deduction rule -. -. C , _G |- -. -. ps => _G |- ps ; see natded . This is Definition NNC in Pfenning p. 17. This rule is valid in classical logic (our logic), but not in intuitionistic logic. (Contributed by DAW, 8-Feb-2017)

	Ref	Expression
Hypothesis	notnotrd.1	$$⊢\phi \to \neg \neg \psi$$
Assertion	notnotrd	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		notnotrd.1	$$⊢\phi \to \neg \neg \psi$$
2		notnotr	$$⊢\neg \neg \psi \to \psi$$
3	1 2	syl	$$⊢\phi \to \psi$$