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 ) ) )

This proof depends on syntax axioms:   <-> wb 105   \/ wo 720   \/ w3o 1008

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

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

This theorem is used by:  3orrot  1015  3orcomb  1018  3mix1  1197  3bior1fd  1393  sotritric  4471  sotritrieq  4472  ordtriexmid  4670  ontriexmidim  4671  acexmidlemcase  6083  nntri3or  6770  nntri2  6771  exmidontriimlem1  7584  elnnz  9666  elznn0  9671  elznn  9672  zapne  9731  nn01to3  10034  elxr  10196  bezoutlemmain  12801  nninfctlemfo  12843  lgsdilem  16363  gausslemma2dlem4  16400