Theorem notnot 144

Description: Double negation introduction. Converse of notnotr 132 and one implication of notnotb 316. 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  316  pm2.13  892  biortn  932  necon2ad  2999  necon4ad  3003  necon4ai  3015  eueq2  3637  ifnot  4431  spthcycl  31985  knoppndvlem10  33470  wl-orel12  34301  cnfn1dd  34921  cnfn2dd  34922  axfrege41  39694  vk15.4j  40420  zfregs2VD  40733  vk15.4jVD  40806  con3ALTVD  40808  stoweidlem39  41886