Theorem notnot 144

Description: Double negation introduction. Converse of notnotr 132 and one implication of notnotb 318. Theorem *2.12 of [WhiteheadRussell] p. 101. This was the sixth axiom of Frege, specifically Proposition 41 of [Frege1879] p. 47. (Contributed by NM, 28-Dec-1992.) (Proof shortened by Wolf Lammen, 2-Mar-2013.)

Assertion

Ref	Expression
notnot	⊢ (𝜑 → ¬ ¬ 𝜑)

Proof of Theorem notnot

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (¬ 𝜑 → ¬ 𝜑)
2	1	con2i 141	1 ⊢ (𝜑 → ¬ ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4

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

This theorem is referenced by:  notnoti  145  notnotd  146  con1d  147  notnotb  318  pm2.13  895  biortn  935  necon2ad  2966  necon4ad  2970  necon4ai  2982  eueq2  3624  ifnot  4472  spthcycl  32607  knoppndvlem10  34250  wl-orel12  35196  cnfn1dd  35810  cnfn2dd  35811  axfrege41  40918  vk15.4j  41607  zfregs2VD  41920  vk15.4jVD  41993  con3ALTVD  41995  stoweidlem39  43047