Theorem notnoti 654

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 638	. 2 ⊢ (𝜑 → ¬ ¬ 𝜑)
3	1, 2	ax-mp 5	1 ⊢ ¬ ¬ 𝜑

This proof depends on syntax axioms:  ¬ wn 3

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 623  ax-in2 624

This theorem is used by:  nbn3  712  fal  1409  ax-9  1584  neirr  2429  dfnul2  3523  rab0  3551