Theorem 3orass 1008

Description: Associative law for triple disjunction. (Contributed by NM, 8-Apr-1994.)

Assertion

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

Proof of Theorem 3orass

Step	Hyp	Ref	Expression
1		df-3or 1006	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
2		orass 775	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	bitri 184	1 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 105   \/ wo 716   \/ w3o 1004

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 717

This theorem depends on definitions:  df-bi 117  df-3or 1006

This theorem is referenced by:  3orrot  1011  3orcomb  1014  3mix1  1193  3bior1fd  1389  sotritric  4447  sotritrieq  4448  ordtriexmid  4645  ontriexmidim  4646  acexmidlemcase  6047  nntri3or  6728  nntri2  6729  exmidontriimlem1  7530  elnnz  9592  elznn0  9597  elznn  9598  zapne  9657  nn01to3  9955  elxr  10115  bezoutlemmain  12702  nninfctlemfo  12744  lgsdilem  15949  gausslemma2dlem4  15986