Theorem notnoti 640

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		notnot 624	. 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-in1 609  ax-in2 610

This theorem is referenced by:  nbn3  695  fal  1355  ax-9  1524  neirr  2349  dfnul2  3416  dfnul3  3417  rab0  3443