Theorem 3ianor 1055

Description: Negated triple conjunction expressed in terms of triple disjunction. (Contributed by Jeff Hankins, 15-Aug-2009.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
3ianor	|- ( -. ( ph /\ ps /\ ch ) <-> ( -. ph \/ -. ps \/ -. ch ) )

Proof of Theorem 3ianor

Step	Hyp	Ref	Expression
1		3anor 1054	. . 3 |- ( ( ph /\ ps /\ ch ) <-> -. ( -. ph \/ -. ps \/ -. ch ) )
2	1	con2bii 347	. 2 |- ( ( -. ph \/ -. ps \/ -. ch ) <-> -. ( ph /\ ps /\ ch ) )
3	2	bicomi 214	1 |- ( -. ( ph /\ ps /\ ch ) <-> ( -. ph \/ -. ps \/ -. ch ) )

Syntax hints:   -. wn 3   <-> wb 196   \/ w3o 1036   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1038  df-3an 1039

This theorem is referenced by:  tppreqb  4336  funtpgOLD  5943  fr3nr  6979  bropopvvv  7255  prinfzo0  12506  elfznelfzo  12573  ssnn0fi  12784  hashtpg  13267  lcmfunsnlem2lem2  15352  prm23ge5  15520  lpni  27332  xrdifh  29542  dvasin  33496  limcicciooub  39869  2zrngnring  41952