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  4427  sotritrieq  4428  ordtriexmid  4625  ontriexmidim  4626  acexmidlemcase  6023  nntri3or  6704  nntri2  6705  exmidontriimlem1  7479  elnnz  9532  elznn0  9537  elznn  9538  zapne  9597  nn01to3  9894  elxr  10054  bezoutlemmain  12630  nninfctlemfo  12672  lgsdilem  15826  gausslemma2dlem4  15863