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  4444  sotritrieq  4445  ordtriexmid  4642  ontriexmidim  4643  acexmidlemcase  6044  nntri3or  6725  nntri2  6726  exmidontriimlem1  7527  elnnz  9583  elznn0  9588  elznn  9589  zapne  9648  nn01to3  9945  elxr  10105  bezoutlemmain  12687  nninfctlemfo  12729  lgsdilem  15887  gausslemma2dlem4  15924