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  4421  sotritrieq  4422  ordtriexmid  4619  ontriexmidim  4620  acexmidlemcase  6013  nntri3or  6661  nntri2  6662  exmidontriimlem1  7436  elnnz  9489  elznn0  9494  elznn  9495  zapne  9554  nn01to3  9851  elxr  10011  bezoutlemmain  12571  nninfctlemfo  12613  lgsdilem  15759  gausslemma2dlem4  15796