Theorem 3orass 1007

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 1005	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
2		orass 774	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	bitri 184	1 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 105   \/ wo 715   \/ w3o 1003

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 716

This theorem depends on definitions:  df-bi 117  df-3or 1005

This theorem is referenced by:  3orrot  1010  3orcomb  1013  3mix1  1192  3bior1fd  1388  sotritric  4423  sotritrieq  4424  ordtriexmid  4621  ontriexmidim  4622  acexmidlemcase  6018  nntri3or  6666  nntri2  6667  exmidontriimlem1  7441  elnnz  9494  elznn0  9499  elznn  9500  zapne  9559  nn01to3  9856  elxr  10016  bezoutlemmain  12592  nninfctlemfo  12634  lgsdilem  15785  gausslemma2dlem4  15822