Theorem notnot 142

Description: Double negation introduction. Converse of notnotr 130 and one implication of notnotb 315. 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 139	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  143  notnotd  144  con1d  145  notnotb  315  pm2.13  897  biortn  937  necon2ad  2948  necon4ad  2952  necon4ai  2964  eueq2  3698  ifnot  4558  spthcycl  35156  knoppndvlem10  36544  wl-orel12  37534  cnfn1dd  38121  cnfn2dd  38122  axfrege41  43835  vk15.4j  44520  zfregs2VD  44832  vk15.4jVD  44905  con3ALTVD  44907  stoweidlem39  46035