Theorem notnoti 574

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 559	. 2 ⊢ (𝜑 → ¬ ¬ 𝜑)
3	1, 2	ax-mp 7	1 ⊢ ¬ ¬ 𝜑

Syntax hints:  ¬ wn 3

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 544  ax-in2 545

This theorem is referenced by:  nbn3  616  fal  1250  ax-9  1424  neirr  2215  dfnul2  3226  dfnul3  3227  rab0  3246