Theorem 3orcomb 990

Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.)

Assertion

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

Proof of Theorem 3orcomb

Step	Hyp	Ref	Expression
1		orcom 730	. . 3 |- ( ( ps \/ ch ) <-> ( ch \/ ps ) )
2	1	orbi2i 764	. 2 |- ( ( ph \/ ( ps \/ ch ) ) <-> ( ph \/ ( ch \/ ps ) ) )
3		3orass 984	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
4		3orass 984	. 2 |- ( ( ph \/ ch \/ ps ) <-> ( ph \/ ( ch \/ ps ) ) )
5	2, 3, 4	3bitr4i 212	1 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ch \/ ps ) )

Syntax hints:   <-> wb 105   \/ wo 710   \/ w3o 980

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 711

This theorem depends on definitions:  df-bi 117  df-3or 982

This theorem is referenced by:  eueq3dc  2947  sotritrieq  4373  exmidontriimlem3  7337  swrdnd  11115