Theorem 3orrot 979

Description: Rotation law for triple disjunction. (Contributed by NM, 4-Apr-1995.)

Assertion

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

Proof of Theorem 3orrot

Step	Hyp	Ref	Expression
1		orcom 723	. 2 |- ( ( ph \/ ( ps \/ ch ) ) <-> ( ( ps \/ ch ) \/ ph ) )
2		3orass 976	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3		df-3or 974	. 2 |- ( ( ps \/ ch \/ ph ) <-> ( ( ps \/ ch ) \/ ph ) )
4	1, 2, 3	3bitr4i 211	1 |- ( ( ph \/ ps \/ ch ) <-> ( ps \/ ch \/ ph ) )

Syntax hints:   <-> wb 104   \/ wo 703   \/ w3o 972

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704

This theorem depends on definitions:  df-bi 116  df-3or 974

This theorem is referenced by:  3mix2  1162  3mix3  1163  eueq3dc  2904  tprot  3676  sotritrieq  4310  exmidontriimlem3  7200  elnnz  9222  elznn  9228  ztri3or0  9254  zapne  9286