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	⊢ ( 𝜑 → ¬ ¬ 𝜓 )
Assertion	notnotrd	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		notnotrd.1	⊢ ( 𝜑 → ¬ ¬ 𝜓 )
2		notnotr	⊢ ( ¬ ¬ 𝜓 → 𝜓 )
3	1 2	syl	⊢ ( 𝜑 → 𝜓 )