Theorem 3orass 1005

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 1003	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
2		orass 772	. 2 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	bitri 184	1 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 105   \/ wo 713   \/ w3o 1001

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 714

This theorem depends on definitions:  df-bi 117  df-3or 1003

This theorem is referenced by:  3orrot  1008  3orcomb  1011  3mix1  1190  3bior1fd  1386  sotritric  4416  sotritrieq  4417  ordtriexmid  4614  ontriexmidim  4615  acexmidlemcase  6005  nntri3or  6652  nntri2  6653  exmidontriimlem1  7419  elnnz  9472  elznn0  9477  elznn  9478  zapne  9537  nn01to3  9829  elxr  9989  bezoutlemmain  12540  nninfctlemfo  12582  lgsdilem  15727  gausslemma2dlem4  15764