Theorem notnot 559

Description: Double negation introduction. Theorem *2.12 of [WhiteheadRussell] p. 101. This one holds for all propositions, but its converse only holds for decidable propositions (see notnotrdc 751). (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 19	. 2 |- ( -. ph -> -. ph )
2	1	con2i 557	1 |- ( ph -> -. -. ph )

Syntax hints:   -. wn 3   -> wi 4

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:  notnotd  560  con3d  561  notnoti  574  pm3.24  627  notnotnot  628  biortn  664  dcn  746  con1dc  753  notnotbdc  766  eueq2dc  2714  difsnpssim  3507  xrlttri3  8718  nltpnft  8730  ngtmnft  8731  bdnthALT  9955