Theorem pm4.13 142

Description: Double negation. Theorem *4.13 of [WhiteheadRussell] p. 117.

Assertion

Ref	Expression
pm4.13	|- (ph <-> -. -. ph)

Proof of Theorem pm4.13

Step	Hyp	Ref	Expression
1		negb 79	. 2 |- (ph -> -. -. ph)
2		nega 78	. 2 |- (-. -. ph -> ph)
3	1, 2	impbi 139	1 |- (ph <-> -. -. ph)

Syntax hints:  -. wn 1   <-> wb 127

This theorem is referenced by:  imor 204  iman 205  ianor 253  ioran 254  oran 255  xor 500  alex 717  sbn2 881  symdif2 1690  chrelat2 5758

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128

metamath.org