Theorem 3orrot 986

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 729	. 2 |- ( ( ph \/ ( ps \/ ch ) ) <-> ( ( ps \/ ch ) \/ ph ) )
2		3orass 983	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3		df-3or 981	. 2 |- ( ( ps \/ ch \/ ph ) <-> ( ( ps \/ ch ) \/ ph ) )
4	1, 2, 3	3bitr4i 212	1 |- ( ( ph \/ ps \/ ch ) <-> ( ps \/ ch \/ ph ) )

Syntax hints:   <-> wb 105   \/ wo 709   \/ w3o 979

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117  df-3or 981

This theorem is referenced by:  3mix2  1169  3mix3  1170  eueq3dc  2934  tprot  3711  sotritrieq  4356  exmidontriimlem3  7283  elnnz  9327  elznn  9333  ztri3or0  9359  zapne  9391