Theorem notnot 136

Description: Double negation introduction. Converse of notnotr 125 and one implication of notnotb 304. 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	|- ( ph -> -. -. ph )

Proof of Theorem notnot

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( -. ph -> -. ph )
2	1	con2i 134	1 |- ( ph -> -. -. ph )

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  137  notnotd  138  con1d  139  con4iOLD  145  notnotb  304  biortn  421  pm2.13  434  nfntOLDOLD  1783  necon2ad  2809  necon4ad  2813  necon4ai  2825  eueq2  3380  ifnot  4133  knoppndvlem10  32512  wl-orel12  33294  cnfn1dd  33894  cnfn2dd  33895  axfrege41  38138  vk15.4j  38734  zfregs2VD  39076  vk15.4jVD  39150  con3ALTVD  39152  stoweidlem39  40256