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Metamath Proof Explorer

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	\|- ( ph -> -. -. ps )
	Assertion	notnotrd	\|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		notnotrd.1	\|- ( ph -> -. -. ps )
2		notnotr	\|- ( -. -. ps -> ps )
3	1 2	syl	\|- ( ph -> ps )