Theorem 3orass 1012

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 1010	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
2		orass 779	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	bitri 184	1 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 105   \/ wo 720   \/ w3o 1008

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 721

This theorem depends on definitions:  df-bi 117  df-3or 1010

This theorem is referenced by:  3orrot  1015  3orcomb  1018  3mix1  1197  3bior1fd  1393  sotritric  4467  sotritrieq  4468  ordtriexmid  4666  ontriexmidim  4667  acexmidlemcase  6074  nntri3or  6760  nntri2  6761  exmidontriimlem1  7571  elnnz  9637  elznn0  9642  elznn  9643  zapne  9702  nn01to3  10000  elxr  10161  bezoutlemmain  12758  nninfctlemfo  12800  lgsdilem  16129  gausslemma2dlem4  16166