Theorem notnoti 115

Description: Infer double negation. (Contributed by NM, 27-Feb-2008.)

Hypothesis

Ref	Expression
negbi.1	⊢ φ

Assertion

Ref	Expression
notnoti	⊢ ¬ ¬ φ

Proof of Theorem notnoti

Step	Hyp	Ref	Expression
1		negbi.1	. 2 ⊢ φ
2		notnot1 114	. 2 ⊢ (φ → ¬ ¬ φ)
3	1, 2	ax-mp 5	1 ⊢ ¬ ¬ φ

Syntax hints:  ¬ wn 3

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  nbn3  337  fal  1322  19.2OLD  1700  ax9dgen  1716  eqtfinrelk  4486  2p1e3c  6156