Theorem notnotnot 635

Description: Triple negation is equivalent to negation. (Contributed by Jim Kingdon, 28-Jul-2018.)

Assertion

Ref	Expression
notnotnot	|- ( -. -. -. ph <-> -. ph )

Proof of Theorem notnotnot

Step	Hyp	Ref	Expression
1		notnot 630	. . 3 |- ( ph -> -. -. ph )
2	1	con3i 633	. 2 |- ( -. -. -. ph -> -. ph )
3		notnot 630	. 2 |- ( -. ph -> -. -. -. ph )
4	2, 3	impbii 126	1 |- ( -. -. -. ph <-> -. ph )

Syntax hints:   -. wn 3   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  stabnot  834  dcnnOLD  850  bj-nnsn  14882