Theorem notnot 591

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 784). (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 589	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 576  ax-in2 577

This theorem is referenced by:  notnotd  592  con3d  593  notnoti  606  pm3.24  659  notnotnot  660  biortn  696  dcn  779  con1dc  786  notnotbdc  799  eueq2dc  2765  ddifstab  3104  xrlttri3  8872  nltpnft  8884  ngtmnft  8885  bdnthALT  10626