Theorem 3ianor 949

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 948	. . 3 |- ((ph /\ ps /\ ch) <-> -. (-. ph \/ -. ps \/ -. ch))
2	1	con2bii 322	. 2 |- ((-. ph \/ -. ps \/ -. ch) <-> -. (ph /\ ps /\ ch))
3	2	bicomi 193	1 |- (-. (ph /\ ps /\ ch) <-> (-. ph \/ -. ps \/ -. ch))

Syntax hints:  -. wn 3   <-> wb 176   \/ w3o 933   /\ w3a 934

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 177  df-or 359  df-an 360  df-3or 935  df-3an 936

This theorem is referenced by: (None)