Theorem notnoti 646

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 630	. 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 615  ax-in2 616

This theorem is referenced by:  nbn3  701  fal  1371  ax-9  1545  neirr  2376  dfnul2  3452  dfnul3  3453  rab0  3479